{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0001","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"04d5205ee7f8a3341028221c8af8e70c39d7650cf52af713f334c7eb50f34437","family_id":"qf-app20-interest-period-update","seed":202610207001,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[50,1],\"rate\":[-2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=50/1, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(50, -1/10, 9/10, 45)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (50, -1/10, 9/10, 45)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0002","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d4afc9910e6dc5c2a71f76fcca44ef4a629bb0a6c879e3b1a23efe7542e963e","family_id":"qf-app20-interest-period-update","seed":202610207002,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[57,2],\"rate\":[-1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=57/2, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(57/2, -1/20, 19/20, 1083/40)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (57/2, -1/20, 19/20, 1083/40)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0003","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0283ac0992d37b2a711c3bd219ef19dc7fa1f6d01084aa255233449a2ea15a77","family_id":"qf-app20-interest-period-update","seed":202610207003,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[64,3],\"rate\":[0,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=64/3, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(64/3, 0, 1, 64/3)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (64/3, 0, 1, 64/3)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0004","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dedb52409590cdac1651853064da506954d7a88a4dbbe5f3f3e0a20530b52ff0","family_id":"qf-app20-interest-period-update","seed":202610207004,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[71,4],\"rate\":[1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=71/4, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(71/4, 1/20, 21/20, 1491/80)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (71/4, 1/20, 21/20, 1491/80)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0005","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"83a49833e01e71ca4061213eebde2f4b157334cff8dfbe17a102778e15f15e8a","family_id":"qf-app20-interest-period-update","seed":202610207005,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[78,1],\"rate\":[2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=78/1, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(78, 1/10, 11/10, 429/5)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (78, 1/10, 11/10, 429/5)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0006","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87bd5f5cd520763cbd55a2cb4982992f15eb884876979f19e318e7542d5cfc8c","family_id":"qf-app20-interest-period-update","seed":202610207006,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[85,2],\"rate\":[-2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=85/2, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(85/2, -1/10, 9/10, 153/4)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (85/2, -1/10, 9/10, 153/4)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0007","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"223bb8258e1fde681df5a8b71b6bc21243c0312c9b88b75114d5c79bcc137afd","family_id":"qf-app20-interest-period-update","seed":202610207007,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[92,3],\"rate\":[-1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=92/3, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(92/3, -1/20, 19/20, 437/15)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (92/3, -1/20, 19/20, 437/15)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0008","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fa3d4a6a093b3623a1b3a429f43c1a8ad0af946814a65c10d09ae99d944f1a24","family_id":"qf-app20-interest-period-update","seed":202610207008,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[99,4],\"rate\":[0,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=99/4, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(99/4, 0, 1, 99/4)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (99/4, 0, 1, 99/4)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0009","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2b2393237804853f0b0c97d66616628b4bf7607518bf109ac5ee093caea959ab","family_id":"qf-app20-interest-period-update","seed":202610207009,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[106,1],\"rate\":[1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=106/1, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(106, 1/20, 21/20, 1113/10)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (106, 1/20, 21/20, 1113/10)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0010","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7d637509194cb9b4f44070a7c03d7ad41b212bd4a61e24cc8d56846b232bb4de","family_id":"qf-app20-interest-period-update","seed":202610207010,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[113,2],\"rate\":[2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=113/2, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(113/2, 1/10, 11/10, 1243/20)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (113/2, 1/10, 11/10, 1243/20)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0011","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e50d04f3268e5795a11d4854bec1d54c6d30fc561bcd87f0fd2089205c81c701","family_id":"qf-app20-interest-period-update","seed":202610207011,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[120,3],\"rate\":[-2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=120/3, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(40, -1/10, 9/10, 36)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (40, -1/10, 9/10, 36)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0012","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2735807b20c031854e3d230d5da9b3c3877e567fbff10b97a98a86d632dcaa83","family_id":"qf-app20-interest-period-update","seed":202610207012,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[127,4],\"rate\":[-1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=127/4, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(127/4, -1/20, 19/20, 2413/80)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (127/4, -1/20, 19/20, 2413/80)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0013","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"85c29fc9941aeeaeadc790d6118ed021714adaa76edde0d98170b77f1d535761","family_id":"qf-app20-interest-period-update","seed":202610207013,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[134,1],\"rate\":[0,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=134/1, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(134, 0, 1, 134)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (134, 0, 1, 134)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0014","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"63bd4ef144c893ff90bead594639d91976f0ee4c2e94d7410cd2dba0ec38401c","family_id":"qf-app20-interest-period-update","seed":202610207014,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[141,2],\"rate\":[1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=141/2, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(141/2, 1/20, 21/20, 2961/40)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (141/2, 1/20, 21/20, 2961/40)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0015","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7f17e3a54afc05a7a83f5a7bb902df2751ffbd6dfd286451221526a4ea43a88","family_id":"qf-app20-interest-period-update","seed":202610207015,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[148,3],\"rate\":[2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=148/3, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(148/3, 1/10, 11/10, 814/15)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (148/3, 1/10, 11/10, 814/15)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0016","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3fccc3f37814adb66f04e27456de6ee0fc84e73e0ca763eb0f1b53b34ba3db17","family_id":"qf-app20-interest-period-update","seed":202610207016,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[155,4],\"rate\":[-2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=155/4, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(155/4, -1/10, 9/10, 279/8)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (155/4, -1/10, 9/10, 279/8)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0017","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"658486044889c3b3b2b38c2f9f5225ff073270c9f351db031a5f7987002e7aae","family_id":"qf-app20-interest-period-update","seed":202610207017,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[162,1],\"rate\":[-1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=162/1, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(162, -1/20, 19/20, 1539/10)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (162, -1/20, 19/20, 1539/10)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0018","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1055677e383ff61bf9417043a81094ecc7086ad2d6ba5b3d55e3dc101792d67","family_id":"qf-app20-interest-period-update","seed":202610207018,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[169,2],\"rate\":[0,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=169/2, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(169/2, 0, 1, 169/2)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (169/2, 0, 1, 169/2)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0019","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a2c22043cfbcc09b2292a5da8477c5fa743b8409d62c9099be461bb89d4af57","family_id":"qf-app20-interest-period-update","seed":202610207019,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[176,3],\"rate\":[1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=176/3, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(176/3, 1/20, 21/20, 308/5)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (176/3, 1/20, 21/20, 308/5)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0020","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf99f5b385d80472fed3829b78b38960db76804d459582505d87809b3197faa4","family_id":"qf-app20-interest-period-update","seed":202610207020,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[183,4],\"rate\":[2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=183/4, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(183/4, 1/10, 11/10, 2013/40)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (183/4, 1/10, 11/10, 2013/40)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0021","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc266b834d170eb51a9f80c66f31d5492c251211863c3e21583f82fbe74dd09b","family_id":"qf-app20-interest-period-update","seed":202610207021,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[190,1],\"rate\":[-2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=190/1, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(190, -1/10, 9/10, 171)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (190, -1/10, 9/10, 171)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0022","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d71953656909a0747d12f876a66c929cb3dd9625afe91ab218c3467016bf3df4","family_id":"qf-app20-interest-period-update","seed":202610207022,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[197,2],\"rate\":[-1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=197/2, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(197/2, -1/20, 19/20, 3743/40)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (197/2, -1/20, 19/20, 3743/40)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0023","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc577f3f4e05f555b56a22f72fc7e0f67b5e8687804ef0c88504794e6e59b0c4","family_id":"qf-app20-interest-period-update","seed":202610207023,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[204,3],\"rate\":[0,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=204/3, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(68, 0, 1, 68)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (68, 0, 1, 68)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0024","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"253ba32a540d715e6e45d125eb707fb81ebdbcf54e432feadb919663b7526a6d","family_id":"qf-app20-interest-period-update","seed":202610207024,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[211,4],\"rate\":[1,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=211/4, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(211/4, 1/20, 21/20, 4431/80)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (211/4, 1/20, 21/20, 4431/80)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0025","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e8fb030619efff501abcc10fd223cfcab306d0b1c96f007f2d23521c299b7a3","family_id":"qf-app20-interest-period-update","seed":202610207025,"semantic_template":"qf-app20-interest-period-update/{\"balance\":[218,1],\"rate\":[2,20]}"},"fields":{"title":"One Exact No-Cash-Flow Compound Period","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=218/1, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).","answer":{"kind":"expression","value":"(218, 1/10, 11/10, 1199/5)","explanation":"Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (218, 1/10, 11/10, 1199/5)."},"skills":["One Exact No-Cash-Flow Compound Period"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0026","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d08a33e25f0fdee515e57a34627cc5c07f32e80aafa101501bfb81c8120e6761","family_id":"qf-app20-interest-future-value","seed":202610207026,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[100,1],\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=100/1, rate=-2/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(100, -1/10, 9/10, 0, 100)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (100, -1/10, 9/10, 0, 100)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0027","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25b11c45e69762e38e3e55c75d62b226cb33f1db0f515e16fb8b5afc7dd81584","family_id":"qf-app20-interest-future-value","seed":202610207027,"semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[105,2],\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=105/2, rate=-1/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(105/2, -1/20, 19/20, 1, 399/8)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (105/2, -1/20, 19/20, 1, 399/8)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0028","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed80ebc4a2ad66606141a52e84117834e7c3d4f316e01a3b0111aa9ebe67d342","family_id":"qf-app20-interest-future-value","seed":202610207028,"semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[110,3],\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=110/3, rate=0/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(110/3, 0, 1, 2, 110/3)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (110/3, 0, 1, 2, 110/3)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0029","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"85126d3761ce0a05698b382f9c294ffc81992b62b9ddcbe35b04a7e57bf2c056","family_id":"qf-app20-interest-future-value","seed":202610207029,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[115,4],\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=115/4, rate=1/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(115/4, 1/20, 21/20, 0, 115/4)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (115/4, 1/20, 21/20, 0, 115/4)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0030","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"683df466b464062050a466141663735271da8a915553e9d7eb3b0a21aede384e","family_id":"qf-app20-interest-future-value","seed":202610207030,"semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[120,1],\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=120/1, rate=2/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(120, 1/10, 11/10, 1, 132)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (120, 1/10, 11/10, 1, 132)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0031","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6d1083b589e4f7f33c0ea8b2f116670bfaf62935d27e4a52c63714afce79d73","family_id":"qf-app20-interest-future-value","seed":202610207031,"semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[125,2],\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=125/2, rate=-2/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(125/2, -1/10, 9/10, 2, 405/8)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (125/2, -1/10, 9/10, 2, 405/8)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0032","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eef83ea917b96fd30d282467a78339736f1663beb90220512c958ff4139485c0","family_id":"qf-app20-interest-future-value","seed":202610207032,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[130,3],\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=130/3, rate=-1/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(130/3, -1/20, 19/20, 0, 130/3)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (130/3, -1/20, 19/20, 0, 130/3)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0033","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"485b9a94ec1baaefbc4e7708c9182bdd05be711c12551c6e1b5c77df72cad3cc","family_id":"qf-app20-interest-future-value","seed":202610207033,"semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[135,4],\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=135/4, rate=0/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(135/4, 0, 1, 1, 135/4)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (135/4, 0, 1, 1, 135/4)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0034","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"16296e3d673ca4ff6632ffc0ec0eebe8f900fc9f401c7116a352c11d66d0f2a4","family_id":"qf-app20-interest-future-value","seed":202610207034,"semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[140,1],\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=140/1, rate=1/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(140, 1/20, 21/20, 2, 3087/20)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (140, 1/20, 21/20, 2, 3087/20)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0035","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ee5443dd1ed5f5bef54cb072ca2d8625a30466bc80a75dda0461993bd93d0fb","family_id":"qf-app20-interest-future-value","seed":202610207035,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[145,2],\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=145/2, rate=2/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(145/2, 1/10, 11/10, 0, 145/2)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (145/2, 1/10, 11/10, 0, 145/2)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0036","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"51bb9cbe4c1578c9498fbff72ff0138de41123177a02091b24570878a0c95e42","family_id":"qf-app20-interest-future-value","seed":202610207036,"semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[150,3],\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=150/3, rate=-2/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(50, -1/10, 9/10, 1, 45)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (50, -1/10, 9/10, 1, 45)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0037","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b0c00699932abd39dd2c035c998c4e33a7bc417201fd14917a2a9249c1c9c27","family_id":"qf-app20-interest-future-value","seed":202610207037,"semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[155,4],\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=155/4, rate=-1/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(155/4, -1/20, 19/20, 2, 11191/320)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (155/4, -1/20, 19/20, 2, 11191/320)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0038","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"146e52c64e0274f0c59f7e4b7e16a4e68e57bc2dcbbc2282eb30b158b67d02ca","family_id":"qf-app20-interest-future-value","seed":202610207038,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[160,1],\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=160/1, rate=0/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(160, 0, 1, 0, 160)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (160, 0, 1, 0, 160)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0039","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac1ddfb426118c6d11251246ba4836a4754429ba34a7da7f9203b42e06bd0582","family_id":"qf-app20-interest-future-value","seed":202610207039,"semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[165,2],\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=165/2, rate=1/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(165/2, 1/20, 21/20, 1, 693/8)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (165/2, 1/20, 21/20, 1, 693/8)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0040","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"390412f5641c2781c84a5a7fc28a0c7d420dde31926627335eb7a6d0c5f3b44d","family_id":"qf-app20-interest-future-value","seed":202610207040,"semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[170,3],\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=170/3, rate=2/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(170/3, 1/10, 11/10, 2, 2057/30)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (170/3, 1/10, 11/10, 2, 2057/30)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0041","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8bc7a98f5d4b8e6c7065cd148884720ca9b8365ffb8a3f33fa5e983d3cbf8e5b","family_id":"qf-app20-interest-future-value","seed":202610207041,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[175,4],\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=175/4, rate=-2/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(175/4, -1/10, 9/10, 0, 175/4)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (175/4, -1/10, 9/10, 0, 175/4)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0042","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1473d46f4bb7d547b48232563df5697baaec8e775aae4ee6cae6510287fc9c0c","family_id":"qf-app20-interest-future-value","seed":202610207042,"semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[180,1],\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=180/1, rate=-1/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(180, -1/20, 19/20, 1, 171)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (180, -1/20, 19/20, 1, 171)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0043","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5ffb5dd241d3fba839de65a48589c396544e0d5e9ae395c43aff15996a063338","family_id":"qf-app20-interest-future-value","seed":202610207043,"semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[185,2],\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=185/2, rate=0/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(185/2, 0, 1, 2, 185/2)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (185/2, 0, 1, 2, 185/2)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0044","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5ea02a439fa7ef839206b2848052bc6eb0cbed192b876d13281b2a130ee927c8","family_id":"qf-app20-interest-future-value","seed":202610207044,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[190,3],\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=190/3, rate=1/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(190/3, 1/20, 21/20, 0, 190/3)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (190/3, 1/20, 21/20, 0, 190/3)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0045","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b294125c821cb57a71617fff5dbc1f7f28c10f8ca5dffc482c81339ce24644bc","family_id":"qf-app20-interest-future-value","seed":202610207045,"semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[195,4],\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=195/4, rate=2/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(195/4, 1/10, 11/10, 1, 429/8)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (195/4, 1/10, 11/10, 1, 429/8)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0046","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9233f4b206a26ab555e42c2f3a6dacbd095d1a1dae971f85c0ff4218452d7ef","family_id":"qf-app20-interest-future-value","seed":202610207046,"semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[200,1],\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=200/1, rate=-2/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(200, -1/10, 9/10, 2, 162)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (200, -1/10, 9/10, 2, 162)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0047","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2055b0e83698c5751613af331937d657c96d73cc1a23a2c8f41feb98a2b8906a","family_id":"qf-app20-interest-future-value","seed":202610207047,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[205,2],\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=205/2, rate=-1/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(205/2, -1/20, 19/20, 0, 205/2)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (205/2, -1/20, 19/20, 0, 205/2)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0048","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0a1e1044957288ba9b361769d30af886009d51e9b51d8b0c0d9e77c51564b9da","family_id":"qf-app20-interest-future-value","seed":202610207048,"semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[210,3],\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=210/3, rate=0/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(70, 0, 1, 1, 70)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (70, 0, 1, 1, 70)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0049","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5cf558be5655adac259e2ecd79ef088d44f2dcf2674b68551436d95fbf922916","family_id":"qf-app20-interest-future-value","seed":202610207049,"semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[215,4],\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=215/4, rate=1/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(215/4, 1/20, 21/20, 2, 18963/320)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (215/4, 1/20, 21/20, 2, 18963/320)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0050","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3671dd5f80803980d3871df5afc33dee98e501a15c309c360d9b14f5caeb0f01","family_id":"qf-app20-interest-future-value","seed":202610207050,"semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[220,1],\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Compound Value Including Zero Periods","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=220/1, rate=2/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).","answer":{"kind":"expression","value":"(220, 1/10, 11/10, 0, 220)","explanation":"Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (220, 1/10, 11/10, 0, 220)."},"skills":["Exact Fixed-Period Compound Value Including Zero Periods"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0051","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"684ba1b927535709ce4e519a80908e1dd01c3aabf9616081acc07bb25dcb1258","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207051,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[101,1],\"periods\":0,\"principal\":[100,1],\"rate\":[-1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=100/1, rate=-1/10, periods=0, candidate=101/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(100, -1/10, 0, 100, 101, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (100, -1/10, 0, 100, 101, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0052","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"accb913dbf45b5e04fb868d53e86eb68b41779eb4bc3828aec26e3207e12af06","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207052,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[399,8],\"periods\":1,\"principal\":[105,2],\"rate\":[-1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=105/2, rate=-1/20, periods=1, candidate=399/8. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(105/2, -1/20, 1, 399/8, 399/8, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (105/2, -1/20, 1, 399/8, 399/8, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0053","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"84dab8d19fa18dabccb63de43dae6cdd030b9ebf6794ab18220211a64705459b","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207053,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[110,3],\"periods\":2,\"principal\":[110,3],\"rate\":[0,1]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=110/3, rate=0/1, periods=2, candidate=110/3. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(110/3, 0, 2, 110/3, 110/3, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (110/3, 0, 2, 110/3, 110/3, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0054","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"139b59a155caa808b71724363db4afc7ab8b7d831b21fc8c560ae9b2630868d5","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207054,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[116,4],\"periods\":0,\"principal\":[115,4],\"rate\":[1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=115/4, rate=1/20, periods=0, candidate=116/4. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(115/4, 1/20, 0, 115/4, 29, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (115/4, 1/20, 0, 115/4, 29, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0055","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"51842b0a1103aac44b4527da73f1d0a157d0de606072e2904389ff2d36f34d5f","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207055,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[132,1],\"periods\":1,\"principal\":[120,1],\"rate\":[1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=120/1, rate=1/10, periods=1, candidate=132/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(120, 1/10, 1, 132, 132, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (120, 1/10, 1, 132, 132, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0056","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e23393eb697e02fe237cb345ef1cea01f248843ac775cd7a3f4fda043fb6be58","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207056,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[405,8],\"periods\":2,\"principal\":[125,2],\"rate\":[-1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=125/2, rate=-1/10, periods=2, candidate=405/8. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(125/2, -1/10, 2, 405/8, 405/8, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (125/2, -1/10, 2, 405/8, 405/8, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0057","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb3be537cb2154f550058616e10ea8085be06e839c630c420a71020c4d511afd","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207057,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[131,3],\"periods\":0,\"principal\":[130,3],\"rate\":[-1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=130/3, rate=-1/20, periods=0, candidate=131/3. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(130/3, -1/20, 0, 130/3, 131/3, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (130/3, -1/20, 0, 130/3, 131/3, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0058","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1526f0960a0b5b5b9ab1f61e16b30f9998e4c938d838cd904a15b41fb4d74bf4","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207058,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[135,4],\"periods\":1,\"principal\":[135,4],\"rate\":[0,1]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=135/4, rate=0/1, periods=1, candidate=135/4. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(135/4, 0, 1, 135/4, 135/4, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (135/4, 0, 1, 135/4, 135/4, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0059","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0111c11fb469d371083d292bdaad4b75d5d96441fc3d87ab2a430075120d821e","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207059,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[3087,20],\"periods\":2,\"principal\":[140,1],\"rate\":[1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=140/1, rate=1/20, periods=2, candidate=3087/20. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(140, 1/20, 2, 3087/20, 3087/20, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (140, 1/20, 2, 3087/20, 3087/20, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0060","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b47a6636f553bd47f4cc04f02c8e18d113507600099cf6f6dbfc0ff7f7cb74c9","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207060,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[146,2],\"periods\":0,\"principal\":[145,2],\"rate\":[1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=145/2, rate=1/10, periods=0, candidate=146/2. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(145/2, 1/10, 0, 145/2, 73, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (145/2, 1/10, 0, 145/2, 73, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0061","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd8acc93a2bf5b9eaeeb9a03e9748f21b215e933e8476303f095916d04669dd1","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207061,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[45,1],\"periods\":1,\"principal\":[50,1],\"rate\":[-1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=50/1, rate=-1/10, periods=1, candidate=45/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(50, -1/10, 1, 45, 45, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (50, -1/10, 1, 45, 45, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0062","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48caf1bf728192b1903726c75908f1dba0e45418f8ac73cfd59d303a6205acc9","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207062,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[11191,320],\"periods\":2,\"principal\":[155,4],\"rate\":[-1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=155/4, rate=-1/20, periods=2, candidate=11191/320. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(155/4, -1/20, 2, 11191/320, 11191/320, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (155/4, -1/20, 2, 11191/320, 11191/320, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0063","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ee59129a032da52722b87c95bd773f243bdcdfc7ed2f40b352e8d4ea531e69a","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207063,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[161,1],\"periods\":0,\"principal\":[160,1],\"rate\":[0,1]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=160/1, rate=0/1, periods=0, candidate=161/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(160, 0, 0, 160, 161, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (160, 0, 0, 160, 161, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0064","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e823ab681e60ccbbf340d11371bf12c785597a6adfefdb7e2d896a55ac1bc053","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207064,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[693,8],\"periods\":1,\"principal\":[165,2],\"rate\":[1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=165/2, rate=1/20, periods=1, candidate=693/8. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(165/2, 1/20, 1, 693/8, 693/8, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (165/2, 1/20, 1, 693/8, 693/8, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0065","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dee71224f41cf95416b0ea49be9337ec3a2da491c5684e1b8991537c2c17d082","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207065,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[2057,30],\"periods\":2,\"principal\":[170,3],\"rate\":[1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=170/3, rate=1/10, periods=2, candidate=2057/30. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(170/3, 1/10, 2, 2057/30, 2057/30, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (170/3, 1/10, 2, 2057/30, 2057/30, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0066","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b2a2c586c36cc814b0306b5543d9360afc7cc6b48c4c5c1561e6b029974419a0","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207066,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[176,4],\"periods\":0,\"principal\":[175,4],\"rate\":[-1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=175/4, rate=-1/10, periods=0, candidate=176/4. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(175/4, -1/10, 0, 175/4, 44, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (175/4, -1/10, 0, 175/4, 44, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0067","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a829e07537d548dea82405cee9f866daf319060883870eb43ff4b17ab6befa66","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207067,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[171,1],\"periods\":1,\"principal\":[180,1],\"rate\":[-1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=180/1, rate=-1/20, periods=1, candidate=171/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(180, -1/20, 1, 171, 171, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (180, -1/20, 1, 171, 171, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0068","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c527b500d21bc1251fa3519febced1eee1b578284bfe8abd8ece16a64868b95","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207068,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[185,2],\"periods\":2,\"principal\":[185,2],\"rate\":[0,1]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=185/2, rate=0/1, periods=2, candidate=185/2. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(185/2, 0, 2, 185/2, 185/2, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (185/2, 0, 2, 185/2, 185/2, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0069","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23d91cdcd1c83567d1388e1d4f776f1d46f9b1f200b859ee2c21ae0040556ec2","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207069,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[191,3],\"periods\":0,\"principal\":[190,3],\"rate\":[1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=190/3, rate=1/20, periods=0, candidate=191/3. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(190/3, 1/20, 0, 190/3, 191/3, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (190/3, 1/20, 0, 190/3, 191/3, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0070","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a8beb5e4e10b71e3889542623cad7b57caa39e0e6ef06704d678367fbbbf5d38","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207070,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[429,8],\"periods\":1,\"principal\":[195,4],\"rate\":[1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=195/4, rate=1/10, periods=1, candidate=429/8. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(195/4, 1/10, 1, 429/8, 429/8, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (195/4, 1/10, 1, 429/8, 429/8, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0071","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ef51b6ee76d6c802bb924e06ec195ddda9d8124016cabb3dc7ae0fddb824e81","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207071,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[162,1],\"periods\":2,\"principal\":[200,1],\"rate\":[-1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=200/1, rate=-1/10, periods=2, candidate=162/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(200, -1/10, 2, 162, 162, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (200, -1/10, 2, 162, 162, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0072","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc7b10e6ed319073cb37e797bcc7eb0e107c99183765b5898d1b6552e45a0d6f","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207072,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[206,2],\"periods\":0,\"principal\":[205,2],\"rate\":[-1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=205/2, rate=-1/20, periods=0, candidate=206/2. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(205/2, -1/20, 0, 205/2, 103, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (205/2, -1/20, 0, 205/2, 103, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0073","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4c7b8cf7ccf34444eb07553ae87b82b1e44f91694438b845984d1630a1bba1c","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207073,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[70,1],\"periods\":1,\"principal\":[70,1],\"rate\":[0,1]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=70/1, rate=0/1, periods=1, candidate=70/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(70, 0, 1, 70, 70, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (70, 0, 1, 70, 70, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0074","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f8c978d3b0f20bd3f843219397ae74df4153aaa0a713a95dd19ce6218de8cd10","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207074,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[18963,320],\"periods\":2,\"principal\":[215,4],\"rate\":[1,20]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=215/4, rate=1/20, periods=2, candidate=18963/320. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(215/4, 1/20, 2, 18963/320, 18963/320, Yes)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (215/4, 1/20, 2, 18963/320, 18963/320, Yes)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0075","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5831d7f072bacb329c113c1e28e6edd0616d91f6202f22b619d5209b9662c29","family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207075,"semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[221,1],\"periods\":0,\"principal\":[220,1],\"rate\":[1,10]}"},"fields":{"title":"Compound Recurrence Value versus a Normalized Candidate","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=220/1, rate=1/10, periods=0, candidate=221/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).","answer":{"kind":"expression","value":"(220, 1/10, 0, 220, 221, No)","explanation":"Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (220, 1/10, 0, 220, 221, No)."},"skills":["Compound Recurrence Value versus a Normalized Candidate"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0076","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0d2bfd580e02cd353915837a1430a55deebfb7eec7b837a041dc1425663f1cfb","family_id":"qf-app20-interest-interest-earned","seed":202610207076,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[100,1],\"rate\":[-2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=100/1, rate=-2/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(100, -1/10, 0, 100, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (100, -1/10, 0, 100, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0077","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c3472e1e01b899356894d42795abdda3a5adaa0f13fa10d1a5c4a0cf520d1ab","family_id":"qf-app20-interest-interest-earned","seed":202610207077,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[105,2],\"rate\":[-1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=105/2, rate=-1/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(105/2, -1/20, 1, 399/8, -21/8)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (105/2, -1/20, 1, 399/8, -21/8)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0078","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0dee114b2a133ecdf5ceba73d32636feb8dd8e67c977014fcebd4a4745532526","family_id":"qf-app20-interest-interest-earned","seed":202610207078,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[110,3],\"rate\":[0,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=110/3, rate=0/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(110/3, 0, 2, 110/3, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (110/3, 0, 2, 110/3, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0079","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c8cbf924ced0ea87977486ecf0c0e3d9bf7cc3ae3fb966acc7e729ce035c71c","family_id":"qf-app20-interest-interest-earned","seed":202610207079,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[115,4],\"rate\":[1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=115/4, rate=1/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(115/4, 1/20, 0, 115/4, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (115/4, 1/20, 0, 115/4, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0080","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e95853a393715b226637f8e3d7258a437807f9ef7f350d493af9a20382117f22","family_id":"qf-app20-interest-interest-earned","seed":202610207080,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[120,1],\"rate\":[2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=120/1, rate=2/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(120, 1/10, 1, 132, 12)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (120, 1/10, 1, 132, 12)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0081","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d78162838bed3640b6d5be3c69ec800227d180016f8e35301d0b91dc147bb369","family_id":"qf-app20-interest-interest-earned","seed":202610207081,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[125,2],\"rate\":[-2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=125/2, rate=-2/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(125/2, -1/10, 2, 405/8, -95/8)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (125/2, -1/10, 2, 405/8, -95/8)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0082","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"718e3643d8dee5c52b54dc541828366fe857553a155cb634f2d778714741952f","family_id":"qf-app20-interest-interest-earned","seed":202610207082,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[130,3],\"rate\":[-1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=130/3, rate=-1/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(130/3, -1/20, 0, 130/3, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (130/3, -1/20, 0, 130/3, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0083","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"50797c32bb428e953d4643fe6a7f2fc32fa99aea4d15678a2806b4c475f35eb6","family_id":"qf-app20-interest-interest-earned","seed":202610207083,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[135,4],\"rate\":[0,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=135/4, rate=0/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(135/4, 0, 1, 135/4, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (135/4, 0, 1, 135/4, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0084","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d0e5bb3ff628864eb60f3084f00c66a61029279540e0d0213ed89005908455c","family_id":"qf-app20-interest-interest-earned","seed":202610207084,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[140,1],\"rate\":[1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=140/1, rate=1/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(140, 1/20, 2, 3087/20, 287/20)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (140, 1/20, 2, 3087/20, 287/20)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0085","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc7f587e2abc8c2309eef26467c80b2624e7074270bda5eeec56db616a1e8bb3","family_id":"qf-app20-interest-interest-earned","seed":202610207085,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[145,2],\"rate\":[2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=145/2, rate=2/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(145/2, 1/10, 0, 145/2, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (145/2, 1/10, 0, 145/2, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0086","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b8fa02110927c945eb94c24d10f0ec860b1ff6ceff87c3a1133c190eab63a9a","family_id":"qf-app20-interest-interest-earned","seed":202610207086,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[150,3],\"rate\":[-2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=150/3, rate=-2/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(50, -1/10, 1, 45, -5)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (50, -1/10, 1, 45, -5)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0087","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e5544a42dad6b28836e153d9c7ddd40e9063e6d1b8badc79d551bdacc73195a2","family_id":"qf-app20-interest-interest-earned","seed":202610207087,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[155,4],\"rate\":[-1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=155/4, rate=-1/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(155/4, -1/20, 2, 11191/320, -1209/320)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (155/4, -1/20, 2, 11191/320, -1209/320)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0088","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"50953063041c509775556dbfce42330164a8147c743ebe0a42be12179b675005","family_id":"qf-app20-interest-interest-earned","seed":202610207088,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[160,1],\"rate\":[0,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=160/1, rate=0/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(160, 0, 0, 160, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (160, 0, 0, 160, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0089","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"47fbd9f5ccba6eb2d67dea2a7bdadfbba0a1577f4d3bcf9871b7851d2f7c3e72","family_id":"qf-app20-interest-interest-earned","seed":202610207089,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[165,2],\"rate\":[1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=165/2, rate=1/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(165/2, 1/20, 1, 693/8, 33/8)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (165/2, 1/20, 1, 693/8, 33/8)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0090","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8cc071ef58ed510d98b678f515e5c539d6196befb8de2e132dfc9336db65af11","family_id":"qf-app20-interest-interest-earned","seed":202610207090,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[170,3],\"rate\":[2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=170/3, rate=2/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(170/3, 1/10, 2, 2057/30, 119/10)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (170/3, 1/10, 2, 2057/30, 119/10)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0091","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"744582dbffa4e52e1e22bc71ab2ab59e6080b85f579e676a428889f08a0adc5f","family_id":"qf-app20-interest-interest-earned","seed":202610207091,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[175,4],\"rate\":[-2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=175/4, rate=-2/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(175/4, -1/10, 0, 175/4, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (175/4, -1/10, 0, 175/4, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0092","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e01efabf1c7fdd09c1005cb0e9b549248e8bba98be007ad678e1f45ccdea373","family_id":"qf-app20-interest-interest-earned","seed":202610207092,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[180,1],\"rate\":[-1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=180/1, rate=-1/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(180, -1/20, 1, 171, -9)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (180, -1/20, 1, 171, -9)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0093","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"229accb21e8597ec3a943b2c0828b15353af500f7a9fb7b19b8abfa8053a35a6","family_id":"qf-app20-interest-interest-earned","seed":202610207093,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[185,2],\"rate\":[0,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=185/2, rate=0/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(185/2, 0, 2, 185/2, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (185/2, 0, 2, 185/2, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0094","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c8957aa4ddc637e4db8d37706d87f9c2c6e6dfd87bd8b29c0949b793b90422d3","family_id":"qf-app20-interest-interest-earned","seed":202610207094,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[190,3],\"rate\":[1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=190/3, rate=1/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(190/3, 1/20, 0, 190/3, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (190/3, 1/20, 0, 190/3, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0095","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dbf6ab99df07c816ecf0fda336bd6da53e926ffd8d3e2308bf6963a2fe23debb","family_id":"qf-app20-interest-interest-earned","seed":202610207095,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[195,4],\"rate\":[2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=195/4, rate=2/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(195/4, 1/10, 1, 429/8, 39/8)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (195/4, 1/10, 1, 429/8, 39/8)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0096","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4bbd8c6b47cf25f88ff4c943cdfc43479036eb83eac121926c15723f9e5cd00d","family_id":"qf-app20-interest-interest-earned","seed":202610207096,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[200,1],\"rate\":[-2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=200/1, rate=-2/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(200, -1/10, 2, 162, -38)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (200, -1/10, 2, 162, -38)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0097","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"21690a22479576b490b0a3db53b5888076c850f7ab5125915c2ffbe1aba0c1c8","family_id":"qf-app20-interest-interest-earned","seed":202610207097,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[205,2],\"rate\":[-1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=205/2, rate=-1/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(205/2, -1/20, 0, 205/2, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (205/2, -1/20, 0, 205/2, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0098","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4bd40393c12bc1ccfb616526f82cebdbe06b8079f37275a736722904c4b23b6d","family_id":"qf-app20-interest-interest-earned","seed":202610207098,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[210,3],\"rate\":[0,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=210/3, rate=0/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(70, 0, 1, 70, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (70, 0, 1, 70, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0099","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"83a1e622e38a4be3df810c1e02b6e2caef7fa4743fe08b411d198c89c2ff720f","family_id":"qf-app20-interest-interest-earned","seed":202610207099,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[215,4],\"rate\":[1,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=215/4, rate=1/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(215/4, 1/20, 2, 18963/320, 1763/320)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (215/4, 1/20, 2, 18963/320, 1763/320)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r07-compound-interest-0100","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"747a7ed129e5b2c847f6aec2b803ba517427abae553f9c34ac4298bce8a8af66","family_id":"qf-app20-interest-interest-earned","seed":202610207100,"semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[220,1],\"rate\":[2,20]}"},"fields":{"title":"Net Compound Interest Can Be Negative","stem":"Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=220/1, rate=2/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.","answer":{"kind":"expression","value":"(220, 1/10, 0, 220, 0)","explanation":"Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (220, 1/10, 0, 220, 0)."},"skills":["Net Compound Interest Can Be Negative"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}