# Compound-interest model

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

With a fixed rate i per period and no additional cash flows, balances satisfy B_(n+1)=(1+i)B_n and hence B_n=B_0(1+i)^n.

mko-compound-interest · definition · v0.10.0



## Mathematical statement

Fix periods, interest timing and rate i per period, with no deposits, withdrawals or fees during the modeled interval. Compound balance updates are B_(n+1)=(1+i)B_n. For 1+i>0, the balance after n periods is B_0(1+i)^n.





## Representative formula (exact TeX)

B(n+1)=M(1+i,B(n))





## Assumptions


- Rate, compounding frequency and period units agree; rates are fixed and there are no cash flows, taxes, fees or rounding.
- Principal is a nonnegative exact rational and 1+i>0. These calculations are not investment advice, quotes or market predictions.





## Symbol scope


- B — end-of-period balance
- n — period index
- i — fixed per-period rate





## Intuition, definition, and misconceptions

Multiply the current balance by the same accumulation factor once per period. Repeating this n times yields the power formula.

Net interest is final balance minus principal. Regular deposits, withdrawals, fees or variable rates require a model other than this single-power formula.

Do not mix annual, monthly, nominal or effective rates; first fix period and conversion conventions.

Do not confuse simple interest B_0(1+n*i) with compound interest B_0(1+i)^n or mix rates from different periods.





## Adopted derivation guide

[Compound-interest model: principal 1000 at 2% per year for three years, compared with simple interest](https://ocme.evemisslab.com/en/derivations/derivation-mko-compound-interest-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites


- [Sequence](https://ocme.evemisslab.com/en/mko/mko-sequence/) — Period balances form a discrete sequence.
- [Natural-number powers and principal square roots](https://ocme.evemisslab.com/en/mko/mko-power-root/) — Accumulation over n periods uses a factor power.
- [Ratio and proportion](https://ocme.evemisslab.com/en/mko/mko-ratio-proportion/) — Rates and accumulation factors are ratios.





## Verification boundary

This slice checks only an exact fixed-period-rate model without cash flows; it is not investment advice or a market forecast.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.





## Next obligation

Develop present-value discounting, nominal/effective rates, annuities and cash-flow timing.





## Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.

[Canonical MKO JSON](https://ocme.evemisslab.com/data/mko/compound-interest.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-compound-interest/index.md)