Fixed-Period Compound Models without Cash Flows
This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.
This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20261013-advance-20261020-r07-compound-interest-foundations · 2026-10-13 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
1. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=50/1, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(50, -1/10, 9/10, 45)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (50, -1/10, 9/10, 45).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
2. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=57/2, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(57/2, -1/20, 19/20, 1083/40)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (57/2, -1/20, 19/20, 1083/40).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
3. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=64/3, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(64/3, 0, 1, 64/3)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (64/3, 0, 1, 64/3).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
4. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=71/4, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(71/4, 1/20, 21/20, 1491/80)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (71/4, 1/20, 21/20, 1491/80).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
5. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=78/1, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(78, 1/10, 11/10, 429/5)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (78, 1/10, 11/10, 429/5).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
6. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=85/2, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(85/2, -1/10, 9/10, 153/4)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (85/2, -1/10, 9/10, 153/4).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
7. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=92/3, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(92/3, -1/20, 19/20, 437/15)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (92/3, -1/20, 19/20, 437/15).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
8. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=99/4, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(99/4, 0, 1, 99/4)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (99/4, 0, 1, 99/4).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
9. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=106/1, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(106, 1/20, 21/20, 1113/10)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (106, 1/20, 21/20, 1113/10).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
10. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=113/2, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(113/2, 1/10, 11/10, 1243/20)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (113/2, 1/10, 11/10, 1243/20).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
11. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=120/3, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(40, -1/10, 9/10, 36)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (40, -1/10, 9/10, 36).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
12. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=127/4, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(127/4, -1/20, 19/20, 2413/80)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (127/4, -1/20, 19/20, 2413/80).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
13. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=134/1, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(134, 0, 1, 134)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (134, 0, 1, 134).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
14. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=141/2, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(141/2, 1/20, 21/20, 2961/40)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (141/2, 1/20, 21/20, 2961/40).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
15. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=148/3, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(148/3, 1/10, 11/10, 814/15)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (148/3, 1/10, 11/10, 814/15).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
16. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=155/4, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(155/4, -1/10, 9/10, 279/8)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (155/4, -1/10, 9/10, 279/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
17. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=162/1, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(162, -1/20, 19/20, 1539/10)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (162, -1/20, 19/20, 1539/10).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
18. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=169/2, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(169/2, 0, 1, 169/2)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (169/2, 0, 1, 169/2).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
19. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=176/3, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(176/3, 1/20, 21/20, 308/5)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (176/3, 1/20, 21/20, 308/5).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
20. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=183/4, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(183/4, 1/10, 11/10, 2013/40)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (183/4, 1/10, 11/10, 2013/40).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
21. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=190/1, rate=-2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(190, -1/10, 9/10, 171)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (190, -1/10, 9/10, 171).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
22. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=197/2, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(197/2, -1/20, 19/20, 3743/40)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (197/2, -1/20, 19/20, 3743/40).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
23. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=204/3, rate=0/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(68, 0, 1, 68)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (68, 0, 1, 68).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
24. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=211/4, rate=1/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(211/4, 1/20, 21/20, 4431/80)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (211/4, 1/20, 21/20, 4431/80).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
25. One Exact No-Cash-Flow Compound Period
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. balance=218/1, rate=2/20. Give (balance, rate, accumulation factor 1+rate, next balance).
View answer and explanation
(218, 1/10, 11/10, 1199/5)
Check the positive accumulation factor and multiply the current balance once; do not substitute a rate from another period convention. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (218, 1/10, 11/10, 1199/5).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-period-update · candidate
26. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=100/1, rate=-2/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(100, -1/10, 9/10, 0, 100)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (100, -1/10, 9/10, 0, 100).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
27. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=105/2, rate=-1/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(105/2, -1/20, 19/20, 1, 399/8)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (105/2, -1/20, 19/20, 1, 399/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
28. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=110/3, rate=0/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(110/3, 0, 1, 2, 110/3)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (110/3, 0, 1, 2, 110/3).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
29. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=115/4, rate=1/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(115/4, 1/20, 21/20, 0, 115/4)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (115/4, 1/20, 21/20, 0, 115/4).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
30. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=120/1, rate=2/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(120, 1/10, 11/10, 1, 132)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (120, 1/10, 11/10, 1, 132).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
31. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=125/2, rate=-2/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(125/2, -1/10, 9/10, 2, 405/8)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (125/2, -1/10, 9/10, 2, 405/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
32. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=130/3, rate=-1/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(130/3, -1/20, 19/20, 0, 130/3)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (130/3, -1/20, 19/20, 0, 130/3).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
33. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=135/4, rate=0/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(135/4, 0, 1, 1, 135/4)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (135/4, 0, 1, 1, 135/4).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
34. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=140/1, rate=1/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(140, 1/20, 21/20, 2, 3087/20)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (140, 1/20, 21/20, 2, 3087/20).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
35. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=145/2, rate=2/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(145/2, 1/10, 11/10, 0, 145/2)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (145/2, 1/10, 11/10, 0, 145/2).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
36. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=150/3, rate=-2/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(50, -1/10, 9/10, 1, 45)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (50, -1/10, 9/10, 1, 45).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
37. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=155/4, rate=-1/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(155/4, -1/20, 19/20, 2, 11191/320)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (155/4, -1/20, 19/20, 2, 11191/320).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
38. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=160/1, rate=0/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(160, 0, 1, 0, 160)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (160, 0, 1, 0, 160).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
39. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=165/2, rate=1/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(165/2, 1/20, 21/20, 1, 693/8)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (165/2, 1/20, 21/20, 1, 693/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
40. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=170/3, rate=2/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(170/3, 1/10, 11/10, 2, 2057/30)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (170/3, 1/10, 11/10, 2, 2057/30).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
41. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=175/4, rate=-2/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(175/4, -1/10, 9/10, 0, 175/4)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (175/4, -1/10, 9/10, 0, 175/4).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
42. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=180/1, rate=-1/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(180, -1/20, 19/20, 1, 171)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (180, -1/20, 19/20, 1, 171).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
43. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=185/2, rate=0/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(185/2, 0, 1, 2, 185/2)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (185/2, 0, 1, 2, 185/2).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
44. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=190/3, rate=1/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(190/3, 1/20, 21/20, 0, 190/3)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (190/3, 1/20, 21/20, 0, 190/3).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
45. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=195/4, rate=2/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(195/4, 1/10, 11/10, 1, 429/8)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (195/4, 1/10, 11/10, 1, 429/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
46. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=200/1, rate=-2/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(200, -1/10, 9/10, 2, 162)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (200, -1/10, 9/10, 2, 162).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
47. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=205/2, rate=-1/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(205/2, -1/20, 19/20, 0, 205/2)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (205/2, -1/20, 19/20, 0, 205/2).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
48. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=210/3, rate=0/20, periods=1. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(70, 0, 1, 1, 70)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (70, 0, 1, 1, 70).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
49. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=215/4, rate=1/20, periods=2. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(215/4, 1/20, 21/20, 2, 18963/320)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (215/4, 1/20, 21/20, 2, 18963/320).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
50. Exact Fixed-Period Compound Value Including Zero Periods
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=220/1, rate=2/20, periods=0. Give (principal, rate, accumulation factor, periods, exact future value).
View answer and explanation
(220, 1/10, 11/10, 0, 220)
Apply the same factor once per period; zero periods preserves principal and this model contains no cash-flow or rounding adjustment. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (220, 1/10, 11/10, 0, 220).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-future-value · candidate
51. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=100/1, rate=-1/10, periods=0, candidate=101/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(100, -1/10, 0, 100, 101, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (100, -1/10, 0, 100, 101, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
52. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=105/2, rate=-1/20, periods=1, candidate=399/8. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(105/2, -1/20, 1, 399/8, 399/8, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (105/2, -1/20, 1, 399/8, 399/8, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
53. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=110/3, rate=0/1, periods=2, candidate=110/3. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(110/3, 0, 2, 110/3, 110/3, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (110/3, 0, 2, 110/3, 110/3, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
54. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=115/4, rate=1/20, periods=0, candidate=116/4. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(115/4, 1/20, 0, 115/4, 29, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (115/4, 1/20, 0, 115/4, 29, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
55. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=120/1, rate=1/10, periods=1, candidate=132/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(120, 1/10, 1, 132, 132, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (120, 1/10, 1, 132, 132, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
56. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=125/2, rate=-1/10, periods=2, candidate=405/8. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(125/2, -1/10, 2, 405/8, 405/8, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (125/2, -1/10, 2, 405/8, 405/8, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
57. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=130/3, rate=-1/20, periods=0, candidate=131/3. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(130/3, -1/20, 0, 130/3, 131/3, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (130/3, -1/20, 0, 130/3, 131/3, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
58. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=135/4, rate=0/1, periods=1, candidate=135/4. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(135/4, 0, 1, 135/4, 135/4, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (135/4, 0, 1, 135/4, 135/4, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
59. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=140/1, rate=1/20, periods=2, candidate=3087/20. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(140, 1/20, 2, 3087/20, 3087/20, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (140, 1/20, 2, 3087/20, 3087/20, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
60. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=145/2, rate=1/10, periods=0, candidate=146/2. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(145/2, 1/10, 0, 145/2, 73, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (145/2, 1/10, 0, 145/2, 73, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
61. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=50/1, rate=-1/10, periods=1, candidate=45/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(50, -1/10, 1, 45, 45, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (50, -1/10, 1, 45, 45, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
62. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=155/4, rate=-1/20, periods=2, candidate=11191/320. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(155/4, -1/20, 2, 11191/320, 11191/320, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (155/4, -1/20, 2, 11191/320, 11191/320, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
63. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=160/1, rate=0/1, periods=0, candidate=161/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(160, 0, 0, 160, 161, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (160, 0, 0, 160, 161, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
64. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=165/2, rate=1/20, periods=1, candidate=693/8. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(165/2, 1/20, 1, 693/8, 693/8, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (165/2, 1/20, 1, 693/8, 693/8, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
65. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=170/3, rate=1/10, periods=2, candidate=2057/30. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(170/3, 1/10, 2, 2057/30, 2057/30, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (170/3, 1/10, 2, 2057/30, 2057/30, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
66. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=175/4, rate=-1/10, periods=0, candidate=176/4. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(175/4, -1/10, 0, 175/4, 44, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (175/4, -1/10, 0, 175/4, 44, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
67. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=180/1, rate=-1/20, periods=1, candidate=171/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(180, -1/20, 1, 171, 171, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (180, -1/20, 1, 171, 171, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
68. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=185/2, rate=0/1, periods=2, candidate=185/2. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(185/2, 0, 2, 185/2, 185/2, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (185/2, 0, 2, 185/2, 185/2, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
69. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=190/3, rate=1/20, periods=0, candidate=191/3. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(190/3, 1/20, 0, 190/3, 191/3, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (190/3, 1/20, 0, 190/3, 191/3, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
70. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=195/4, rate=1/10, periods=1, candidate=429/8. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(195/4, 1/10, 1, 429/8, 429/8, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (195/4, 1/10, 1, 429/8, 429/8, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
71. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=200/1, rate=-1/10, periods=2, candidate=162/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(200, -1/10, 2, 162, 162, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (200, -1/10, 2, 162, 162, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
72. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=205/2, rate=-1/20, periods=0, candidate=206/2. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(205/2, -1/20, 0, 205/2, 103, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (205/2, -1/20, 0, 205/2, 103, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
73. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=70/1, rate=0/1, periods=1, candidate=70/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(70, 0, 1, 70, 70, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (70, 0, 1, 70, 70, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
74. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=215/4, rate=1/20, periods=2, candidate=18963/320. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(215/4, 1/20, 2, 18963/320, 18963/320, Yes)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (215/4, 1/20, 2, 18963/320, 18963/320, Yes).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
75. Compound Recurrence Value versus a Normalized Candidate
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=220/1, rate=1/10, periods=0, candidate=221/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).
View answer and explanation
(220, 1/10, 0, 220, 221, No)
Compute the declared compound model and compare exact values; simple interest is a different model. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (220, 1/10, 0, 220, 221, No).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-recurrence-power-audit · candidate
76. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=100/1, rate=-2/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(100, -1/10, 0, 100, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (100, -1/10, 0, 100, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
77. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=105/2, rate=-1/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(105/2, -1/20, 1, 399/8, -21/8)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (105/2, -1/20, 1, 399/8, -21/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
78. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=110/3, rate=0/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(110/3, 0, 2, 110/3, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (110/3, 0, 2, 110/3, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
79. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=115/4, rate=1/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(115/4, 1/20, 0, 115/4, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (115/4, 1/20, 0, 115/4, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
80. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=120/1, rate=2/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(120, 1/10, 1, 132, 12)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (120, 1/10, 1, 132, 12).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
81. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=125/2, rate=-2/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(125/2, -1/10, 2, 405/8, -95/8)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (125/2, -1/10, 2, 405/8, -95/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
82. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=130/3, rate=-1/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(130/3, -1/20, 0, 130/3, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (130/3, -1/20, 0, 130/3, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
83. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=135/4, rate=0/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(135/4, 0, 1, 135/4, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (135/4, 0, 1, 135/4, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
84. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=140/1, rate=1/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(140, 1/20, 2, 3087/20, 287/20)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (140, 1/20, 2, 3087/20, 287/20).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
85. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=145/2, rate=2/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(145/2, 1/10, 0, 145/2, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (145/2, 1/10, 0, 145/2, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
86. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=150/3, rate=-2/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(50, -1/10, 1, 45, -5)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (50, -1/10, 1, 45, -5).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
87. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=155/4, rate=-1/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(155/4, -1/20, 2, 11191/320, -1209/320)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (155/4, -1/20, 2, 11191/320, -1209/320).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
88. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=160/1, rate=0/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(160, 0, 0, 160, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (160, 0, 0, 160, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
89. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=165/2, rate=1/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(165/2, 1/20, 1, 693/8, 33/8)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (165/2, 1/20, 1, 693/8, 33/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
90. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=170/3, rate=2/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(170/3, 1/10, 2, 2057/30, 119/10)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (170/3, 1/10, 2, 2057/30, 119/10).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
91. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=175/4, rate=-2/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(175/4, -1/10, 0, 175/4, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (175/4, -1/10, 0, 175/4, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
92. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=180/1, rate=-1/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(180, -1/20, 1, 171, -9)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (180, -1/20, 1, 171, -9).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
93. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=185/2, rate=0/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(185/2, 0, 2, 185/2, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (185/2, 0, 2, 185/2, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
94. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=190/3, rate=1/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(190/3, 1/20, 0, 190/3, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (190/3, 1/20, 0, 190/3, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
95. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=195/4, rate=2/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(195/4, 1/10, 1, 429/8, 39/8)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (195/4, 1/10, 1, 429/8, 39/8).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
96. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=200/1, rate=-2/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(200, -1/10, 2, 162, -38)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (200, -1/10, 2, 162, -38).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
97. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=205/2, rate=-1/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(205/2, -1/20, 0, 205/2, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (205/2, -1/20, 0, 205/2, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
98. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=210/3, rate=0/20, periods=1. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(70, 0, 1, 70, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (70, 0, 1, 70, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
99. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=215/4, rate=1/20, periods=2. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(215/4, 1/20, 2, 18963/320, 1763/320)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (215/4, 1/20, 2, 18963/320, 1763/320).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
100. Net Compound Interest Can Be Negative
Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=220/1, rate=2/20, periods=0. Give (principal, rate, periods, future value, future value−principal). A permitted negative rate may produce negative net interest.
View answer and explanation
(220, 1/10, 0, 220, 0)
Subtract principal without taking an absolute value or clipping the result to zero. This is not investment advice or a market forecast. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (220, 1/10, 0, 220, 0).
Reviewed step-by-step derivation
Compound-interest model · qf-app20-interest-interest-earned · candidate
Canonical question JSONL · English JSONL · Validation report