Compound-interest model

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

The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.

Prerequisites

• Sequence — Period balances form a discrete sequence.
• Natural-number powers and principal square roots — Accumulation over n periods uses a factor power.
• Ratio and 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.