Question 1867: One Exact No-Cash-Flow Compound Period

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. balance=162/1, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).

• 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. balance=162/1, rate=-1/20. Give (balance, rate, accumulation factor 1+rate, next balance).

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, -1/20)

accumulation factor = 19/20

per-period rate=-1/20; factor=19/20>0

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

current balance=162

next balance=162·19/20

next balance := mul(162, 19/20)

next balance = 1539/10

Reverse checks

• S004 · premise_and_result_audit — Recompute next balance 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

(162, -1/20, 19/20, 1539/10)

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.