{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261022-r02-present-value-discounting-0001","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"35045f0c622725b179591d7ffc48ced3ff8fc6252b44d5f0a928fdcd159d1a62","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222001,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[100,1],\"rate\":[-2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=100/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(100, -1/10, 9/10, 1000/9)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (100, -1/10, 9/10, 1000/9)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0002","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9f009fd5ee84087c7a4ec7b5714f8a2d7c7957b44a942cf1a0cba7a49ad70c3","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222002,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[103,2],\"rate\":[-1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=103/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(103/2, -1/20, 19/20, 1030/19)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (103/2, -1/20, 19/20, 1030/19)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0003","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ac2867cf4a5873d66f31185fe809a1fd9856f47d02f9a19a2815b9077042ad4","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222003,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[106,3],\"rate\":[0,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=106/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(106/3, 0, 1, 106/3)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (106/3, 0, 1, 106/3)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0004","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ee0c452621a8e5de66c5573fc24545c338d96d94a80550bc1b236d529259d99","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222004,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[109,1],\"rate\":[1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=109/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(109, 1/20, 21/20, 2180/21)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (109, 1/20, 21/20, 2180/21)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0005","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0d5aa1f87dee0c400ff3e76a82924e9797d1d6a666fdf5fedb5f04f546950f8d","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222005,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[112,2],\"rate\":[2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=112/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(56, 1/10, 11/10, 560/11)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (56, 1/10, 11/10, 560/11)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0006","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e2619182ba31792ea4fee6b1bbdbbcfa0c4d9a12d19d1fa872d798c3ae2a2234","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222006,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[115,3],\"rate\":[-2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=115/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(115/3, -1/10, 9/10, 1150/27)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (115/3, -1/10, 9/10, 1150/27)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0007","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"144397b38804fbcb1d172d783ef215cce4ce6fba326d9ec7a7dc64dd61578a21","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222007,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[118,1],\"rate\":[-1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=118/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(118, -1/20, 19/20, 2360/19)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (118, -1/20, 19/20, 2360/19)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0008","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a605cab6655186fbf3a13103c806d813d3568350089a1d3d958b4e3e52ce75ce","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222008,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[121,2],\"rate\":[0,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=121/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(121/2, 0, 1, 121/2)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (121/2, 0, 1, 121/2)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0009","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c1e98a788b3a918fd8fb358754ffb2b351cb4c5057fcbbc1edee7f86fbc7b456","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222009,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[124,3],\"rate\":[1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=124/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(124/3, 1/20, 21/20, 2480/63)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (124/3, 1/20, 21/20, 2480/63)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0010","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7a27ed9b1141c646247d50581eadb9adba425d5bf895d2916a10afde3c616b8f","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222010,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[127,1],\"rate\":[2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=127/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(127, 1/10, 11/10, 1270/11)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (127, 1/10, 11/10, 1270/11)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0011","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65342ad38c41697fd9d41857fc8b66e9c2bc50dad1bbd838a4a02e4086eadbde","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222011,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[130,2],\"rate\":[-2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=130/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(65, -1/10, 9/10, 650/9)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (65, -1/10, 9/10, 650/9)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0012","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"855eee33140472f7e4dd9609571cefa193926dce3871ca1e3a75ea84e3cd95e0","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222012,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[133,3],\"rate\":[-1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=133/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(133/3, -1/20, 19/20, 140/3)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (133/3, -1/20, 19/20, 140/3)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0013","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6ab22189496b818c245fc04187cc619e0150e56169377fc117cde408719c1a6","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222013,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[136,1],\"rate\":[0,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=136/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(136, 0, 1, 136)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (136, 0, 1, 136)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0014","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b8f6aa38c60a9a25d324cf1bc3750352b93d10e19998d4aeddb3993c0334b86","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222014,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[139,2],\"rate\":[1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=139/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(139/2, 1/20, 21/20, 1390/21)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (139/2, 1/20, 21/20, 1390/21)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0015","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a487cf753830fb2c78f5c08e2ca86088785d45c404bc81ff71f2b1d75f0ab277","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222015,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[142,3],\"rate\":[2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=142/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(142/3, 1/10, 11/10, 1420/33)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (142/3, 1/10, 11/10, 1420/33)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0016","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0cf9ab8bc232e8cce5473e7ce0fdf122f4635a4b1294f4222afc7dde02d27c8","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222016,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[145,1],\"rate\":[-2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=145/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(145, -1/10, 9/10, 1450/9)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (145, -1/10, 9/10, 1450/9)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0017","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"775ed3f64ffce9bc4e6c284b6be0d8471c985eb1a6235b60bf2c83f1d446637e","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222017,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[148,2],\"rate\":[-1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=148/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(74, -1/20, 19/20, 1480/19)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (74, -1/20, 19/20, 1480/19)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0018","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e5e75f091da55fedc378bf86b526e29ca4005325c9614f5f4c8cbca9b1fc842","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222018,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[151,3],\"rate\":[0,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=151/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(151/3, 0, 1, 151/3)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (151/3, 0, 1, 151/3)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0019","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c7a703a6f795de4e6f172d16da89a604c4e505cf7a45f5e7a4676f42335b39c","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222019,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[154,1],\"rate\":[1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=154/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(154, 1/20, 21/20, 440/3)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (154, 1/20, 21/20, 440/3)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0020","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ea2af2ba63892d89544e514f3b80cc86d25c093f6c984abd3a62f3c9f6b06821","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222020,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[157,2],\"rate\":[2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=157/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(157/2, 1/10, 11/10, 785/11)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (157/2, 1/10, 11/10, 785/11)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0021","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c40f5b4c7e0dea5f8b3e6a56865f739b80a6c543a6230770a572e13466238498","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222021,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[160,3],\"rate\":[-2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=160/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(160/3, -1/10, 9/10, 1600/27)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (160/3, -1/10, 9/10, 1600/27)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0022","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"17693150c3146946a07ab8c822d488e2a2ff4d0956276494e8727a0712c74bd7","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222022,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[163,1],\"rate\":[-1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=163/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(163, -1/20, 19/20, 3260/19)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (163, -1/20, 19/20, 3260/19)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0023","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"619f6c03ae88bd6e042902b8bd2e9b224065e74d7595dad685f3cb687a9e2be9","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222023,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[166,2],\"rate\":[0,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=166/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(83, 0, 1, 83)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (83, 0, 1, 83)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0024","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"38023195a82ce1def0769d1d6c8f0c39e3f01785fd6d1a934ab723a1a3918f88","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222024,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[169,3],\"rate\":[1,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=169/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(169/3, 1/20, 21/20, 3380/63)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (169/3, 1/20, 21/20, 3380/63)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0025","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6475586d2f5750fa9a3db9ef351aaf3e1af1817ed8fd3e43c32ea72ff76c49dd","family_id":"qf-str22-presentvalue-one-period-discount","seed":202610222025,"semantic_template":"qf-str22-presentvalue-one-period-discount/{\"future\":[172,1],\"rate\":[2,20]}"},"fields":{"title":"One-Period Discount by a Positive Accumulation Factor","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=172/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.","answer":{"kind":"expression","value":"(172, 1/10, 11/10, 1720/11)","explanation":"Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (172, 1/10, 11/10, 1720/11)."},"skills":["One-Period Discount by a Positive Accumulation Factor"],"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-20261022-r02-present-value-discounting-0026","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6edab821e7354a0ebeedaa26a1ce6a28b008b19c53c46dab3f27d4197d7ff37","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222026,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[100,1],\"periods\":0,\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=100/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(100, -1/10, 0, 1, 100)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (100, -1/10, 0, 1, 100)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0027","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4d1312b05a6615fd5387c9eaf3265b8928ebe4b8c812b5b3b8efcf85adabee8d","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222027,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[103,2],\"periods\":1,\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=103/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(103/2, -1/20, 1, 19/20, 1030/19)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (103/2, -1/20, 1, 19/20, 1030/19)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0028","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"072f38fe801247e66ba17ce3d521ad8cbf25a921923149ec802cb2db5990c507","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222028,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[106,3],\"periods\":2,\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=106/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(106/3, 0, 2, 1, 106/3)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (106/3, 0, 2, 1, 106/3)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0029","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c137ba6e66272445063e96015dbe0aa7308d902e4f7af4d26fff9fe40d50b491","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222029,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[109,1],\"periods\":0,\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=109/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(109, 1/20, 0, 1, 109)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (109, 1/20, 0, 1, 109)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0030","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"73b146dd6801514980c60c42fe3cc99a7bac7ad645dec4de2c67b6c7b5182e61","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222030,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[112,2],\"periods\":1,\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=112/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(56, 1/10, 1, 11/10, 560/11)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (56, 1/10, 1, 11/10, 560/11)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0031","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf830bbea7355717211a21a9b212e2aee814dbfc50f02b3c8669cdcc78c7a687","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222031,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[115,3],\"periods\":2,\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=115/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(115/3, -1/10, 2, 81/100, 11500/243)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (115/3, -1/10, 2, 81/100, 11500/243)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0032","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5f1d9ea97fb938bce54a29f33dce24dc8709a720795318de5d15d536a94194ac","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222032,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[118,1],\"periods\":0,\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=118/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(118, -1/20, 0, 1, 118)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (118, -1/20, 0, 1, 118)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0033","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7147146e09bbf86eb4b9e0e9ec225465de2fbc4ffd0f8b121e0d36dafbd1278c","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222033,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[121,2],\"periods\":1,\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=121/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(121/2, 0, 1, 1, 121/2)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (121/2, 0, 1, 1, 121/2)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0034","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fbd99e156f7db09fadc10938cc754be5034302ad83f2c6d1d33c4d63f24bc578","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222034,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[124,3],\"periods\":2,\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=124/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(124/3, 1/20, 2, 441/400, 49600/1323)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (124/3, 1/20, 2, 441/400, 49600/1323)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0035","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"98883c2d9e39af95733db23ca42f59182fb8a9249e9f6cf686c37a4653408e03","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222035,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[127,1],\"periods\":0,\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=127/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(127, 1/10, 0, 1, 127)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (127, 1/10, 0, 1, 127)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0036","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c0f4976a1665a9fbfad75523c02cab3f00ce03f02211212e92e52eaa98779a0d","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222036,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[130,2],\"periods\":1,\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=130/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(65, -1/10, 1, 9/10, 650/9)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (65, -1/10, 1, 9/10, 650/9)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0037","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52b12c220ef94cb6fe5ee41adade95a12e29a237c5703fe80fcd4ef2b10c7f90","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222037,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[133,3],\"periods\":2,\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=133/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(133/3, -1/20, 2, 361/400, 2800/57)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (133/3, -1/20, 2, 361/400, 2800/57)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0038","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"063a9a4c6390dbb904e0bb673bd3deb942581ca62b93e6a5483a30ae8d200f1a","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222038,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[136,1],\"periods\":0,\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=136/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(136, 0, 0, 1, 136)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (136, 0, 0, 1, 136)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0039","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e84b5813c56c7dd5ecfc7d51a9edc5afcd787b16222e8b0f4b4f176cea646df3","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222039,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[139,2],\"periods\":1,\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=139/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(139/2, 1/20, 1, 21/20, 1390/21)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (139/2, 1/20, 1, 21/20, 1390/21)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0040","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7aec53e0bd3ed5432bfe5fe20902b6041743613a7e5f4a217def4fc4b5c58ba","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222040,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[142,3],\"periods\":2,\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=142/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(142/3, 1/10, 2, 121/100, 14200/363)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (142/3, 1/10, 2, 121/100, 14200/363)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0041","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ff5dafbdcf73cbb5dedbe6523af1ff532e21c8e2d574340cbcd8fec38be843a9","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222041,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[145,1],\"periods\":0,\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=145/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(145, -1/10, 0, 1, 145)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (145, -1/10, 0, 1, 145)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0042","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a4725331eb136d2784a486921c0ef83da408477c12401f04567fcaace8ab30e1","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222042,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[148,2],\"periods\":1,\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=148/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(74, -1/20, 1, 19/20, 1480/19)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (74, -1/20, 1, 19/20, 1480/19)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0043","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54763d2b8d4bbc0e3aebbbd2eae8e7b9a7604eeac41f9bf82d8b7bdf1111aa5a","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222043,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[151,3],\"periods\":2,\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=151/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(151/3, 0, 2, 1, 151/3)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (151/3, 0, 2, 1, 151/3)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0044","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4eb0a7cfc6a29b86a0c90ef21cac498064b814de3ddbd18137b10ef56b5eee8","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222044,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[154,1],\"periods\":0,\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=154/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(154, 1/20, 0, 1, 154)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (154, 1/20, 0, 1, 154)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0045","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"80f89ee3062c8de4c82d33e8561e5e2dbf34ecf994146bde57077d78dd95dbbe","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222045,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[157,2],\"periods\":1,\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=157/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(157/2, 1/10, 1, 11/10, 785/11)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (157/2, 1/10, 1, 11/10, 785/11)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0046","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8b20194b4be99e1c358a9fa4e24a25cee5a98326113d77ded9373ecd6d0729cb","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222046,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[160,3],\"periods\":2,\"rate\":[-2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=160/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(160/3, -1/10, 2, 81/100, 16000/243)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (160/3, -1/10, 2, 81/100, 16000/243)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0047","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"21c7fa3d2f069a01c48ec4fbf94829baa3d4c3c27aaffe29cdff242a9f9a2d42","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222047,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[163,1],\"periods\":0,\"rate\":[-1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=163/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(163, -1/20, 0, 1, 163)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (163, -1/20, 0, 1, 163)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0048","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da06b235cc545c0200e5d79c18471c1ffb792e7968846313dcabb141a6887e25","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222048,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[166,2],\"periods\":1,\"rate\":[0,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=166/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(83, 0, 1, 1, 83)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (83, 0, 1, 1, 83)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0049","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da98a338780eef1a8866670a84dc9623af0ba0973be4c5e599c5547615aa6624","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222049,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[169,3],\"periods\":2,\"rate\":[1,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=169/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(169/3, 1/20, 2, 441/400, 67600/1323)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (169/3, 1/20, 2, 441/400, 67600/1323)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0050","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81104b080ae54922b53669671990d108c5eb5e4fb15426fe9dfec277994a0749","family_id":"qf-str22-presentvalue-n-period-discount","seed":202610222050,"semantic_template":"qf-str22-presentvalue-n-period-discount/{\"future\":[172,1],\"periods\":0,\"rate\":[2,20]}"},"fields":{"title":"Exact Fixed-Period Discount Including Zero Periods","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=172/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.","answer":{"kind":"expression","value":"(172, 1/10, 0, 1, 172)","explanation":"Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (172, 1/10, 0, 1, 172)."},"skills":["Exact Fixed-Period Discount 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-20261022-r02-present-value-discounting-0051","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b5bc12db1113df03abecc106e92d41bf39b31893d6b77c1fd5b231f746f8bcf6","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222051,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[50,1],\"rate\":[-2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=50/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(50, -1/10, 0, 50, 50, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (50, -1/10, 0, 50, 50, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0052","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"71d1d4d6b04d4099ae021cff0904e14d1143c8ce20cfa4103a58930f3667d9c4","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222052,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[52,2],\"rate\":[-1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=52/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(26, -1/20, 1, 247/10, 26, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (26, -1/20, 1, 247/10, 26, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0053","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c919eba4d87b40ba4f565112da0eb7f658da87f94145433879461a2a272a448c","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222053,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[54,3],\"rate\":[0,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=54/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(18, 0, 2, 18, 18, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (18, 0, 2, 18, 18, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0054","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74c10ffb38c8ca3579e2851a6d8e32b2a4db9452861a52394f6d1f4344f2609a","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222054,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[56,1],\"rate\":[1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=56/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(56, 1/20, 0, 56, 56, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (56, 1/20, 0, 56, 56, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0055","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12c2a1b9d512922ddc30f70925e19e4be0149ec077e596028f6abe70dee7922a","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222055,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[58,2],\"rate\":[2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=58/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(29, 1/10, 1, 319/10, 29, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (29, 1/10, 1, 319/10, 29, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0056","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa721b9199ad713c95ae0e89a78d5d370521406c7d0ff33235ad64c0dfb496a0","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222056,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[60,3],\"rate\":[-2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=60/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(20, -1/10, 2, 81/5, 20, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (20, -1/10, 2, 81/5, 20, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0057","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"950ec16c0ec0a7c1a3b499516af912f21770bfedc7f123586b78975d8db40682","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222057,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[62,1],\"rate\":[-1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=62/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(62, -1/20, 0, 62, 62, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (62, -1/20, 0, 62, 62, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0058","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74f48f63ae2873cf7840504551f95f17d4dc82918da5150f9f869288e3102f15","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222058,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[64,2],\"rate\":[0,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=64/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(32, 0, 1, 32, 32, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (32, 0, 1, 32, 32, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0059","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40dc35d0642786b01580c2dbf57ba3363e9d460d17256babc8ff592aa1c9a635","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222059,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[66,3],\"rate\":[1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=66/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(22, 1/20, 2, 4851/200, 22, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (22, 1/20, 2, 4851/200, 22, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0060","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b2cf28a2925f65065304a4df13ca84f375178591702b89004befbee2ae775c6","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222060,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[68,1],\"rate\":[2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=68/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(68, 1/10, 0, 68, 68, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (68, 1/10, 0, 68, 68, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0061","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a0e247615ebbe0de5423f450b35caabfe8ada62d93973eb2971bc2c85cfdbee4","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222061,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[70,2],\"rate\":[-2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=70/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(35, -1/10, 1, 63/2, 35, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (35, -1/10, 1, 63/2, 35, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0062","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1fc591507c4918c7194ced7195f5e0416029c37d3ec16f553313d2c629ba0be1","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222062,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[72,3],\"rate\":[-1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=72/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(24, -1/20, 2, 1083/50, 24, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (24, -1/20, 2, 1083/50, 24, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0063","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bdc918e7caf54adc7d45ccaa29d7f8bddd809af85fdaba907daa32aa0c642109","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222063,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[74,1],\"rate\":[0,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=74/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(74, 0, 0, 74, 74, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (74, 0, 0, 74, 74, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0064","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6f93aa0043f4076bf107f4cbae81eac28e5f9e3819878f0f17507dbd5ba2c1d","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222064,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[76,2],\"rate\":[1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=76/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(38, 1/20, 1, 399/10, 38, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (38, 1/20, 1, 399/10, 38, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0065","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9fea3512f3736b24b49a4e849d9b0246d4cbe848da7b34f83e4c9313443bb1d7","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222065,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[78,3],\"rate\":[2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=78/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(26, 1/10, 2, 1573/50, 26, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (26, 1/10, 2, 1573/50, 26, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0066","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c790727c523c9286fa66642073d2df7ba98985eea55ff3ef69127cf02426cc75","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222066,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[80,1],\"rate\":[-2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=80/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(80, -1/10, 0, 80, 80, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (80, -1/10, 0, 80, 80, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0067","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"85465a18d329539ce4f74d693c9cbd1d021e9c31a6fd37eb57f2d2d3cd86ad17","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222067,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[82,2],\"rate\":[-1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=82/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(41, -1/20, 1, 779/20, 41, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (41, -1/20, 1, 779/20, 41, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0068","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b8476e3e3cec9f7caac78cf450ff34e1b84b1516b81258e9e0a2aed0f2d299f","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222068,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[84,3],\"rate\":[0,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=84/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(28, 0, 2, 28, 28, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (28, 0, 2, 28, 28, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0069","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8d2b990d79ce19232a1d8d5088c9c13081c49f4d09d27eae7f9c0e6d61fbe83f","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222069,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[86,1],\"rate\":[1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=86/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(86, 1/20, 0, 86, 86, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (86, 1/20, 0, 86, 86, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0070","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"94f0f9a34f564370c3a31108451b56d9fc5a156ddfe0f1fb67f1263c5597dfbd","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222070,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[88,2],\"rate\":[2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=88/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(44, 1/10, 1, 242/5, 44, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (44, 1/10, 1, 242/5, 44, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0071","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78da7596b8989d462b69bdcbd522cfc4f991dad48da741cd1010e98574eba908","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222071,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[90,3],\"rate\":[-2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=90/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(30, -1/10, 2, 243/10, 30, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (30, -1/10, 2, 243/10, 30, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0072","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5e97129ac1c97dd661779b859948ea04e7b20a75ef0efc0f22144926ee73f12","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222072,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[92,1],\"rate\":[-1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=92/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(92, -1/20, 0, 92, 92, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (92, -1/20, 0, 92, 92, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0073","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"192b87551433d52b954a65d28ede8aa212457dde955b2d167271978de4c6202b","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222073,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":1,\"principal\":[94,2],\"rate\":[0,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=94/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(47, 0, 1, 47, 47, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (47, 0, 1, 47, 47, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0074","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7559361f83ce98d47c4808d32263b53e3983a59f40dd35a8d759046601624db8","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222074,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":2,\"principal\":[96,3],\"rate\":[1,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=96/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(32, 1/20, 2, 882/25, 32, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (32, 1/20, 2, 882/25, 32, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0075","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a6755f464258060fa1879a8ef8ef41a34ceb053845da5220191470725665f7c","family_id":"qf-str22-presentvalue-forward-backward-audit","seed":202610222075,"semantic_template":"qf-str22-presentvalue-forward-backward-audit/{\"periods\":0,\"principal\":[98,1],\"rate\":[2,20]}"},"fields":{"title":"Compound and Discount with the Same Factor and Period Count","stem":"Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=98/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).","answer":{"kind":"expression","value":"(98, 1/10, 0, 98, 98, Yes)","explanation":"Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (98, 1/10, 0, 98, 98, Yes)."},"skills":["Compound and Discount with the Same Factor and Period Count"],"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-20261022-r02-present-value-discounting-0076","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"587828807b1099e613c4c767aa8e80de2557a7eab8ca0edb9c1436cfddf50c90","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222076,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[101,1],\"future\":[100,1],\"periods\":0,\"rate\":[-1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=100/1, periods=0, nonnegative candidate=101/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(100, -1/10, 0, 100, 101, No)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (100, -1/10, 0, 100, 101, No)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0077","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28f679c878d722c03f0a2e3bda693f1f5b4d14753a7f58aeee1e1614dc5cfb75","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222077,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[1030,19],\"future\":[103,2],\"periods\":1,\"rate\":[-1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=103/2, periods=1, nonnegative candidate=1030/19. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(103/2, -1/20, 1, 1030/19, 1030/19, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (103/2, -1/20, 1, 1030/19, 1030/19, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0078","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8f56e8d1e15b75df02d6b2bc242770e1f6b4b647780432cd7556e9f602cdea44","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222078,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[106,3],\"future\":[106,3],\"periods\":2,\"rate\":[0,1]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=106/3, periods=2, nonnegative candidate=106/3. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(106/3, 0, 2, 106/3, 106/3, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (106/3, 0, 2, 106/3, 106/3, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0079","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8d3b390d31fa2f5632371132a92cef3fb8ed6bb874b0a0f468c3c321e2ed3738","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222079,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[109,1],\"future\":[109,1],\"periods\":0,\"rate\":[1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=109/1, periods=0, nonnegative candidate=109/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(109, 1/20, 0, 109, 109, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (109, 1/20, 0, 109, 109, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0080","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dfeb041ae9848b2724086a984a4f5ffd0d599df6472d2f211fe07f7e3943d2bc","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222080,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[561,11],\"future\":[56,1],\"periods\":1,\"rate\":[1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=56/1, periods=1, nonnegative candidate=561/11. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(56, 1/10, 1, 560/11, 51, No)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (56, 1/10, 1, 560/11, 51, No)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0081","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6c6adb9beb789e1a4b889ddda872e7a6b8836ac77c742081fcf2203b4d44cd2","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222081,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[11500,243],\"future\":[115,3],\"periods\":2,\"rate\":[-1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=115/3, periods=2, nonnegative candidate=11500/243. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(115/3, -1/10, 2, 11500/243, 11500/243, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (115/3, -1/10, 2, 11500/243, 11500/243, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0082","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7b625bc9939843e2b32594e7009b36a06f64a1ecf703f683c67ee1b8e901d32","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222082,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[118,1],\"future\":[118,1],\"periods\":0,\"rate\":[-1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=118/1, periods=0, nonnegative candidate=118/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(118, -1/20, 0, 118, 118, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (118, -1/20, 0, 118, 118, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0083","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64dfe4954930ad14a17766660c569ed40b6aa2be99a472faec5298828996667f","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222083,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[121,2],\"future\":[121,2],\"periods\":1,\"rate\":[0,1]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=121/2, periods=1, nonnegative candidate=121/2. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(121/2, 0, 1, 121/2, 121/2, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (121/2, 0, 1, 121/2, 121/2, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0084","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9fcbeb4cec83fceff161141a7a6b75f420461985f7ff9c6068b69ae9a8347f6c","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222084,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[49601,1323],\"future\":[124,3],\"periods\":2,\"rate\":[1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=124/3, periods=2, nonnegative candidate=49601/1323. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(124/3, 1/20, 2, 49600/1323, 49601/1323, No)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (124/3, 1/20, 2, 49600/1323, 49601/1323, No)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0085","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"021eaeeb8f614ed1dc7dd45c45bc0b341e2df202dd34822c542ae0eacc03049b","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222085,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[127,1],\"future\":[127,1],\"periods\":0,\"rate\":[1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=127/1, periods=0, nonnegative candidate=127/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(127, 1/10, 0, 127, 127, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (127, 1/10, 0, 127, 127, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0086","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a0dd5634d60d3862034f537d3af72a59cab05f9b9a31e37cdc2209bc23506e98","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222086,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[650,9],\"future\":[65,1],\"periods\":1,\"rate\":[-1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=65/1, periods=1, nonnegative candidate=650/9. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(65, -1/10, 1, 650/9, 650/9, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (65, -1/10, 1, 650/9, 650/9, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0087","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"32128d55233b3f3a577597082c584dfad0bdb8c11eeb8cbd6ff9f8d85fafe8dc","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222087,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[2800,57],\"future\":[133,3],\"periods\":2,\"rate\":[-1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=133/3, periods=2, nonnegative candidate=2800/57. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(133/3, -1/20, 2, 2800/57, 2800/57, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (133/3, -1/20, 2, 2800/57, 2800/57, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0088","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74dd158120143224345374cb7522b303186dc8ccedaa0adefd08d8e64fdbca2f","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222088,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[137,1],\"future\":[136,1],\"periods\":0,\"rate\":[0,1]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=136/1, periods=0, nonnegative candidate=137/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(136, 0, 0, 136, 137, No)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (136, 0, 0, 136, 137, No)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0089","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb8bdf59293e93194f7c988c8c23b4c4e4712aacae1a9406176eabab76f58763","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222089,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[1390,21],\"future\":[139,2],\"periods\":1,\"rate\":[1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=139/2, periods=1, nonnegative candidate=1390/21. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(139/2, 1/20, 1, 1390/21, 1390/21, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (139/2, 1/20, 1, 1390/21, 1390/21, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0090","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"049acb585972b569b4c08f15248c04b87c1575f7558dd0858ea38ff95f87f48c","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222090,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[14200,363],\"future\":[142,3],\"periods\":2,\"rate\":[1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=142/3, periods=2, nonnegative candidate=14200/363. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(142/3, 1/10, 2, 14200/363, 14200/363, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (142/3, 1/10, 2, 14200/363, 14200/363, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0091","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce624508c86ee9bf4d3d7aec0aa8e8f7b9a470ed3a2dc722f9f344d57ff3ef2f","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222091,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[145,1],\"future\":[145,1],\"periods\":0,\"rate\":[-1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=145/1, periods=0, nonnegative candidate=145/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(145, -1/10, 0, 145, 145, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (145, -1/10, 0, 145, 145, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0092","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d60aae5326b4b1da563843ab12253bf9c2a71afc3080d745f1f6f1a6c253ce7b","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222092,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[1481,19],\"future\":[74,1],\"periods\":1,\"rate\":[-1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=74/1, periods=1, nonnegative candidate=1481/19. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(74, -1/20, 1, 1480/19, 1481/19, No)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (74, -1/20, 1, 1480/19, 1481/19, No)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0093","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"153a33e5ee73f9b2613570024524dea43aa247bb33d058d2e26416e6c01c072b","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222093,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[151,3],\"future\":[151,3],\"periods\":2,\"rate\":[0,1]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=151/3, periods=2, nonnegative candidate=151/3. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(151/3, 0, 2, 151/3, 151/3, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (151/3, 0, 2, 151/3, 151/3, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0094","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3925c604817e009d6ab530a87e0aeaf40d3962951e2d199a1c14a140da9c5993","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222094,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[154,1],\"future\":[154,1],\"periods\":0,\"rate\":[1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=154/1, periods=0, nonnegative candidate=154/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(154, 1/20, 0, 154, 154, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (154, 1/20, 0, 154, 154, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0095","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42d0df91b7283c6ce19076331d76a6e777a4314d2021b08ff204032aea85b980","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222095,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[785,11],\"future\":[157,2],\"periods\":1,\"rate\":[1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=157/2, periods=1, nonnegative candidate=785/11. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(157/2, 1/10, 1, 785/11, 785/11, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (157/2, 1/10, 1, 785/11, 785/11, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0096","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e4ebb6283c569d1e547d3a759f734cd1cf73a9a7845df53dd691b5f2286dd0a","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222096,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[16001,243],\"future\":[160,3],\"periods\":2,\"rate\":[-1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=160/3, periods=2, nonnegative candidate=16001/243. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(160/3, -1/10, 2, 16000/243, 16001/243, No)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (160/3, -1/10, 2, 16000/243, 16001/243, No)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0097","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29e7920b8134714221174ae0a9e7880348933362fa2a77d65537a5ceec3f4e14","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222097,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[163,1],\"future\":[163,1],\"periods\":0,\"rate\":[-1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=163/1, periods=0, nonnegative candidate=163/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(163, -1/20, 0, 163, 163, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (163, -1/20, 0, 163, 163, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0098","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a14f04c30db213a751066350918cd988c0fbd6bed76f94285eac2f27a42c60f4","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222098,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[83,1],\"future\":[83,1],\"periods\":1,\"rate\":[0,1]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=83/1, periods=1, nonnegative candidate=83/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(83, 0, 1, 83, 83, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (83, 0, 1, 83, 83, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0099","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"71e59c8201a5419979d838607e15e5f2fd97ba98934f59f4eb7e436699087050","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222099,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[67600,1323],\"future\":[169,3],\"periods\":2,\"rate\":[1,20]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=169/3, periods=2, nonnegative candidate=67600/1323. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(169/3, 1/20, 2, 67600/1323, 67600/1323, Yes)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (169/3, 1/20, 2, 67600/1323, 67600/1323, Yes)."},"skills":["Compare a Normalized Candidate Present Value"],"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-20261022-r02-present-value-discounting-0100","batch_id":"batch-20261013-advance-20261022-r02-present-value-discounting-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6537928375cd9793166395b5ef2dcc19de669534d310506ccd4603f3fba98048","family_id":"qf-str22-presentvalue-candidate-audit","seed":202610222100,"semantic_template":"qf-str22-presentvalue-candidate-audit/{\"candidate\":[173,1],\"future\":[172,1],\"periods\":0,\"rate\":[1,10]}"},"fields":{"title":"Compare a Normalized Candidate Present Value","stem":"Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=172/1, periods=0, nonnegative candidate=173/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).","answer":{"kind":"expression","value":"(172, 1/10, 0, 172, 173, No)","explanation":"Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (172, 1/10, 0, 172, 173, No)."},"skills":["Compare a Normalized Candidate Present Value"],"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."}}