Compound interest formula with examples

Basic compound interest formula

The basic formula is A = P × (1 + r)^t. A is the final amount, P the principal, r the effective rate per period and t the number of periods.

Worked example

$10,000 growing at an effective 5% a year for ten years gives 10,000 × 1.05^10 = $16,288.95 before fees, inflation and taxes.

Nominal rate and multiple compounding periods

For a nominal annual rate j compounded m times per year, A = P × (1 + j/m)^(m×t). The equivalent effective annual rate is (1 + j/m)^m − 1.

Formula with recurring contributions

For equal end-of-period deposits, FV = PMT × ((1 + r)^n − 1) / r. Beginning-of-period deposits multiply this result by (1 + r). Capliz uses a period-by-period engine for more complex cases.

Errors and edge cases

Do not divide an effective annual rate by twelve and treat it as nominal. At a zero rate, final capital equals principal plus contributions. Capliz rounds for display, not after each simulated period.

How to check the result

Keep the rate and time unit consistent, distinguish an effective annual rate from a nominal rate, and state when each contribution is made. A manual result should match the Capliz projection when principal, cash flows, timing, rate type and period are identical.

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