Exact Fixed-Period Present Values and Compound-Discount Roundtrips
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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-20261022-r02-present-value-discounting-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-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=100/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(100, -1/10, 9/10, 1000/9)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (100, -1/10, 9/10, 1000/9).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
2. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=103/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(103/2, -1/20, 19/20, 1030/19)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (103/2, -1/20, 19/20, 1030/19).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
3. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=106/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(106/3, 0, 1, 106/3)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (106/3, 0, 1, 106/3).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
4. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=109/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(109, 1/20, 21/20, 2180/21)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (109, 1/20, 21/20, 2180/21).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
5. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=112/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(56, 1/10, 11/10, 560/11)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (56, 1/10, 11/10, 560/11).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
6. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=115/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(115/3, -1/10, 9/10, 1150/27)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (115/3, -1/10, 9/10, 1150/27).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
7. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=118/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(118, -1/20, 19/20, 2360/19)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (118, -1/20, 19/20, 2360/19).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
8. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=121/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(121/2, 0, 1, 121/2)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (121/2, 0, 1, 121/2).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
9. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=124/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(124/3, 1/20, 21/20, 2480/63)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (124/3, 1/20, 21/20, 2480/63).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
10. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=127/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(127, 1/10, 11/10, 1270/11)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (127, 1/10, 11/10, 1270/11).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
11. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=130/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(65, -1/10, 9/10, 650/9)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (65, -1/10, 9/10, 650/9).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
12. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=133/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(133/3, -1/20, 19/20, 140/3)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (133/3, -1/20, 19/20, 140/3).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
13. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=136/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(136, 0, 1, 136)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (136, 0, 1, 136).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
14. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=139/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(139/2, 1/20, 21/20, 1390/21)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (139/2, 1/20, 21/20, 1390/21).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
15. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=142/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(142/3, 1/10, 11/10, 1420/33)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (142/3, 1/10, 11/10, 1420/33).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
16. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=145/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(145, -1/10, 9/10, 1450/9)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (145, -1/10, 9/10, 1450/9).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
17. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=148/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(74, -1/20, 19/20, 1480/19)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (74, -1/20, 19/20, 1480/19).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
18. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=151/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(151/3, 0, 1, 151/3)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (151/3, 0, 1, 151/3).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
19. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=154/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(154, 1/20, 21/20, 440/3)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (154, 1/20, 21/20, 440/3).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
20. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=157/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(157/2, 1/10, 11/10, 785/11)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (157/2, 1/10, 11/10, 785/11).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
21. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=160/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(160/3, -1/10, 9/10, 1600/27)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (160/3, -1/10, 9/10, 1600/27).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
22. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=163/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(163, -1/20, 19/20, 3260/19)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (163, -1/20, 19/20, 3260/19).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
23. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=166/2. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(83, 0, 1, 83)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (83, 0, 1, 83).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
24. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=169/3. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(169/3, 1/20, 21/20, 3380/63)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (169/3, 1/20, 21/20, 3380/63).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
25. One-Period Discount by a Positive Accumulation Factor
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future amount=172/1. Give (future amount,rate,1+rate,present value=future/(1+rate)). A permitted negative rate may make present value exceed future value.
View answer and explanation
(172, 1/10, 11/10, 1720/11)
Discount by division, not multiplication; a positive accumulation factor does not require a nonnegative rate. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (172, 1/10, 11/10, 1720/11).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-one-period-discount · candidate
26. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=100/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(100, -1/10, 0, 1, 100)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (100, -1/10, 0, 1, 100).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
27. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=103/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(103/2, -1/20, 1, 19/20, 1030/19)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (103/2, -1/20, 1, 19/20, 1030/19).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
28. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=106/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(106/3, 0, 2, 1, 106/3)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (106/3, 0, 2, 1, 106/3).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
29. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=109/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(109, 1/20, 0, 1, 109)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (109, 1/20, 0, 1, 109).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
30. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=112/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(56, 1/10, 1, 11/10, 560/11)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (56, 1/10, 1, 11/10, 560/11).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
31. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=115/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(115/3, -1/10, 2, 81/100, 11500/243)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (115/3, -1/10, 2, 81/100, 11500/243).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
32. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=118/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(118, -1/20, 0, 1, 118)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (118, -1/20, 0, 1, 118).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
33. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=121/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(121/2, 0, 1, 1, 121/2)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (121/2, 0, 1, 1, 121/2).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
34. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=124/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(124/3, 1/20, 2, 441/400, 49600/1323)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (124/3, 1/20, 2, 441/400, 49600/1323).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
35. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=127/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(127, 1/10, 0, 1, 127)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (127, 1/10, 0, 1, 127).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
36. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=130/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(65, -1/10, 1, 9/10, 650/9)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (65, -1/10, 1, 9/10, 650/9).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
37. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=133/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(133/3, -1/20, 2, 361/400, 2800/57)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (133/3, -1/20, 2, 361/400, 2800/57).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
38. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=136/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(136, 0, 0, 1, 136)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (136, 0, 0, 1, 136).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
39. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=139/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(139/2, 1/20, 1, 21/20, 1390/21)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (139/2, 1/20, 1, 21/20, 1390/21).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
40. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=142/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(142/3, 1/10, 2, 121/100, 14200/363)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (142/3, 1/10, 2, 121/100, 14200/363).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
41. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=145/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(145, -1/10, 0, 1, 145)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (145, -1/10, 0, 1, 145).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
42. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=148/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(74, -1/20, 1, 19/20, 1480/19)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (74, -1/20, 1, 19/20, 1480/19).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
43. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=151/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(151/3, 0, 2, 1, 151/3)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (151/3, 0, 2, 1, 151/3).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
44. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=154/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(154, 1/20, 0, 1, 154)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (154, 1/20, 0, 1, 154).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
45. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=157/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(157/2, 1/10, 1, 11/10, 785/11)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (157/2, 1/10, 1, 11/10, 785/11).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
46. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=160/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(160/3, -1/10, 2, 81/100, 16000/243)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (160/3, -1/10, 2, 81/100, 16000/243).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
47. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=163/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(163, -1/20, 0, 1, 163)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (163, -1/20, 0, 1, 163).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
48. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=166/2, periods=1≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(83, 0, 1, 1, 83)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (83, 0, 1, 1, 83).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
49. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=169/3, periods=2≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(169/3, 1/20, 2, 441/400, 67600/1323)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (169/3, 1/20, 2, 441/400, 67600/1323).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
50. Exact Fixed-Period Discount Including Zero Periods
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=172/1, periods=0≥0. Give (future,rate,periods,(1+rate)^periods,present value). Zero periods gives accumulation 1 and preserves the amount.
View answer and explanation
(172, 1/10, 0, 1, 172)
Use the same rate and period convention throughout and divide by the accumulation power. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (172, 1/10, 0, 1, 172).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-n-period-discount · candidate
51. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=50/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(50, -1/10, 0, 50, 50, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (50, -1/10, 0, 50, 50, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
52. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=52/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(26, -1/20, 1, 247/10, 26, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (26, -1/20, 1, 247/10, 26, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
53. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=54/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(18, 0, 2, 18, 18, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (18, 0, 2, 18, 18, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
54. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=56/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(56, 1/20, 0, 56, 56, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (56, 1/20, 0, 56, 56, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
55. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=58/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(29, 1/10, 1, 319/10, 29, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (29, 1/10, 1, 319/10, 29, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
56. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=60/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(20, -1/10, 2, 81/5, 20, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (20, -1/10, 2, 81/5, 20, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
57. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=62/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(62, -1/20, 0, 62, 62, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (62, -1/20, 0, 62, 62, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
58. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=64/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(32, 0, 1, 32, 32, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (32, 0, 1, 32, 32, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
59. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=66/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(22, 1/20, 2, 4851/200, 22, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (22, 1/20, 2, 4851/200, 22, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
60. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=68/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(68, 1/10, 0, 68, 68, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (68, 1/10, 0, 68, 68, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
61. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=70/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(35, -1/10, 1, 63/2, 35, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (35, -1/10, 1, 63/2, 35, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
62. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=72/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(24, -1/20, 2, 1083/50, 24, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (24, -1/20, 2, 1083/50, 24, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
63. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=74/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(74, 0, 0, 74, 74, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (74, 0, 0, 74, 74, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
64. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=76/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(38, 1/20, 1, 399/10, 38, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (38, 1/20, 1, 399/10, 38, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
65. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=78/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(26, 1/10, 2, 1573/50, 26, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (26, 1/10, 2, 1573/50, 26, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
66. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=80/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(80, -1/10, 0, 80, 80, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (80, -1/10, 0, 80, 80, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
67. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=82/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(41, -1/20, 1, 779/20, 41, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (41, -1/20, 1, 779/20, 41, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
68. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=84/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(28, 0, 2, 28, 28, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (28, 0, 2, 28, 28, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
69. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=86/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(86, 1/20, 0, 86, 86, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (86, 1/20, 0, 86, 86, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
70. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=88/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(44, 1/10, 1, 242/5, 44, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (44, 1/10, 1, 242/5, 44, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
71. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=90/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(30, -1/10, 2, 243/10, 30, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (30, -1/10, 2, 243/10, 30, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
72. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=92/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(92, -1/20, 0, 92, 92, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (92, -1/20, 0, 92, 92, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
73. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=0/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=94/2, periods=1. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(47, 0, 1, 47, 47, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (47, 0, 1, 47, 47, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
74. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=96/3, periods=2. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(32, 1/20, 2, 882/25, 32, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (32, 1/20, 2, 882/25, 32, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
75. Compound and Discount with the Same Factor and Period Count
Use a fixed rate i=2/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. principal=98/1, periods=0. Give (principal,rate,periods,compounded future amount,recovered present amount,exact recovery?).
View answer and explanation
(98, 1/10, 0, 98, 98, Yes)
Compound then discount using identical parameters. An exact algebraic roundtrip within this model is not a prediction of market returns. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (98, 1/10, 0, 98, 98, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-forward-backward-audit · candidate
76. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=100/1, periods=0, nonnegative candidate=101/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(100, -1/10, 0, 100, 101, No)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (100, -1/10, 0, 100, 101, No).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
77. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=103/2, periods=1, nonnegative candidate=1030/19. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(103/2, -1/20, 1, 1030/19, 1030/19, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (103/2, -1/20, 1, 1030/19, 1030/19, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
78. Compare a Normalized Candidate Present Value
Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=106/3, periods=2, nonnegative candidate=106/3. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(106/3, 0, 2, 106/3, 106/3, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (106/3, 0, 2, 106/3, 106/3, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
79. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=109/1, periods=0, nonnegative candidate=109/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(109, 1/20, 0, 109, 109, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (109, 1/20, 0, 109, 109, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
80. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=56/1, periods=1, nonnegative candidate=561/11. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(56, 1/10, 1, 560/11, 51, No)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (56, 1/10, 1, 560/11, 51, No).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
81. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=115/3, periods=2, nonnegative candidate=11500/243. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(115/3, -1/10, 2, 11500/243, 11500/243, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (115/3, -1/10, 2, 11500/243, 11500/243, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
82. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=118/1, periods=0, nonnegative candidate=118/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(118, -1/20, 0, 118, 118, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (118, -1/20, 0, 118, 118, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
83. Compare a Normalized Candidate Present Value
Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=121/2, periods=1, nonnegative candidate=121/2. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(121/2, 0, 1, 121/2, 121/2, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (121/2, 0, 1, 121/2, 121/2, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
84. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=124/3, periods=2, nonnegative candidate=49601/1323. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(124/3, 1/20, 2, 49600/1323, 49601/1323, No)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (124/3, 1/20, 2, 49600/1323, 49601/1323, No).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
85. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=127/1, periods=0, nonnegative candidate=127/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(127, 1/10, 0, 127, 127, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (127, 1/10, 0, 127, 127, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
86. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=65/1, periods=1, nonnegative candidate=650/9. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(65, -1/10, 1, 650/9, 650/9, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (65, -1/10, 1, 650/9, 650/9, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
87. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=133/3, periods=2, nonnegative candidate=2800/57. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(133/3, -1/20, 2, 2800/57, 2800/57, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (133/3, -1/20, 2, 2800/57, 2800/57, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
88. Compare a Normalized Candidate Present Value
Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=136/1, periods=0, nonnegative candidate=137/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(136, 0, 0, 136, 137, No)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (136, 0, 0, 136, 137, No).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
89. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=139/2, periods=1, nonnegative candidate=1390/21. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(139/2, 1/20, 1, 1390/21, 1390/21, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (139/2, 1/20, 1, 1390/21, 1390/21, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
90. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=142/3, periods=2, nonnegative candidate=14200/363. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(142/3, 1/10, 2, 14200/363, 14200/363, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (142/3, 1/10, 2, 14200/363, 14200/363, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
91. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=145/1, periods=0, nonnegative candidate=145/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(145, -1/10, 0, 145, 145, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (145, -1/10, 0, 145, 145, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
92. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=74/1, periods=1, nonnegative candidate=1481/19. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(74, -1/20, 1, 1480/19, 1481/19, No)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (74, -1/20, 1, 1480/19, 1481/19, No).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
93. Compare a Normalized Candidate Present Value
Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=151/3, periods=2, nonnegative candidate=151/3. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(151/3, 0, 2, 151/3, 151/3, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (151/3, 0, 2, 151/3, 151/3, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
94. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=154/1, periods=0, nonnegative candidate=154/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(154, 1/20, 0, 154, 154, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (154, 1/20, 0, 154, 154, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
95. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=157/2, periods=1, nonnegative candidate=785/11. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(157/2, 1/10, 1, 785/11, 785/11, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (157/2, 1/10, 1, 785/11, 785/11, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
96. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=160/3, periods=2, nonnegative candidate=16001/243. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(160/3, -1/10, 2, 16000/243, 16001/243, No)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (160/3, -1/10, 2, 16000/243, 16001/243, No).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
97. Compare a Normalized Candidate Present Value
Use a fixed rate i=-1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=163/1, periods=0, nonnegative candidate=163/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(163, -1/20, 0, 163, 163, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (163, -1/20, 0, 163, 163, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
98. Compare a Normalized Candidate Present Value
Use a fixed rate i=0/1 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=83/1, periods=1, nonnegative candidate=83/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(83, 0, 1, 83, 83, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (83, 0, 1, 83, 83, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
99. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/20 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=169/3, periods=2, nonnegative candidate=67600/1323. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(169/3, 1/20, 2, 67600/1323, 67600/1323, Yes)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (169/3, 1/20, 2, 67600/1323, 67600/1323, Yes).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
100. Compare a Normalized Candidate Present Value
Use a fixed rate i=1/10 per declared period, with 1+i>0, fixed period conventions and no cash flows, fees, taxes or rounding. Amounts are nonnegative exact rationals. Use exact rationals, normalize denominator signs, reduce fractions and omit /1 for integer outputs. This is not investment advice, a quote or a market forecast. future=172/1, periods=0, nonnegative candidate=173/1. Give (future,rate,periods,exact present value,normalized candidate,equal?).
View answer and explanation
(172, 1/10, 0, 172, 173, No)
Normalize both rational values before comparison, retaining the declared period conventions. This explicit exact slice is not a general theorem or empirical assertion. The exact result, retaining the requested order, is (172, 1/10, 0, 172, 173, No).
Reviewed step-by-step derivation
Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate
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