Question 1896: Compound Recurrence Value versus a Normalized Candidate

Original question and givens

Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=200/1, rate=-1/10, periods=2, candidate=162/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).

• G001 — Use one fixed exact rate per declared period and no deposits, withdrawals, fees, taxes or rounding. Rate and period conventions agree; balances/principal are nonnegative and 1+rate>0. This is not investment advice, a quote or a market forecast. Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. principal=200/1, rate=-1/10, periods=2, candidate=162/1. Give (principal, rate, periods, exact future value, normalized nonnegative candidate, equal?).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-compound-interest

Step-by-step derivation

accumulation factor := sum(1, -1/10)

accumulation factor = 9/10

per-period rate=-1/10; factor=9/10>0

fixed-period exact recurrence B_(k+1)=(1+r)B_k

B₀=200; periods=2

0 periods leave the principal unchanged

B_1 := mul(200, 9/10)

B_1 = 180

B_2 := mul(180, 9/10)

B_2 = 162

B₀=P; B_(k+1)=(1+r)B_k

B_n=P(1+r)^n by induction

(9/10)^2

(1+r)^n = 81/100

future balance := mul(200, 81/100)

future balance = 162

model future=162; candidate=162

candidate agrees: Yes

Reverse checks

• S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S008 · premise_and_result_audit — Recompute future balance with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S005 · premise_and_result_audit — Recompute B_2 with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute B_1 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Recompute accumulation factor with exact rational arithmetic, not rounded decimals.

Result

(200, -1/10, 2, 162, 162, Yes)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.