# 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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0001/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0002/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0003/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0004/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0005/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0006/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0007/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0008/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0009/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0010/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0011/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0012/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0013/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0014/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0015/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0016/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0017/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0018/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0019/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0020/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0021/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0022/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0023/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0024/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0025/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0026/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0027/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0028/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0029/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0030/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0031/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0032/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0033/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0034/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0035/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0036/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0037/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0038/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0039/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0040/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0041/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0042/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0043/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0044/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0045/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0046/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0047/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0048/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0049/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0050/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0051/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0052/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0053/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0054/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0055/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0056/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0057/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0058/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0059/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0060/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0061/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0062/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0063/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0064/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0065/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0066/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0067/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0068/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0069/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0070/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0071/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0072/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0073/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0074/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0075/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0076/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0077/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0078/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0079/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0080/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0081/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0082/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0083/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0084/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0085/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0086/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0087/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0088/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0089/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0090/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0091/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0092/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0093/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0094/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0095/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0096/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0097/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0098/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0099/)

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](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261022-r02-present-value-discounting-0100/)

Present value and discounting · qf-str22-presentvalue-candidate-audit · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261022-r02-present-value-discounting-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261013-advance-20261022-r02-present-value-discounting-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261022-r02-present-value-discounting-foundations/validation-report.json)