Compound Interest

Choose future value or savings goal. Both use the same starting amount, deposit and nominal annual interest rate. Interest compounding and deposit cadence are separate: changing annual to daily compounding does not turn a monthly deposit into a daily deposit.

Annual growth is (1+r/n)^n for n interest periods per year, or e^r for continuous compounding. Deposits occur at the end of each selected deposit interval. Between crediting dates, equivalent fractional-period growth is used; this is not a bank day-count contract. A partial final deposit interval earns interest but receives no extra deposit.

With 1000 initially, 10% annual compounding and 100 deposited annually, the value after two years is 1420. The starting amount plus deposits is shown separately from earned interest. Tiny nonzero returns use scientific notation rather than silently rounding to zero.

The goal mode finds the first completed deposit interval at or above the target, using both selected cadences. It shows that date’s actual balance, including any overshoot. It does not interpolate a fictitious partial deposit. Existing wealth may already meet the target; a negative-return saving ceiling may make a target unreachable.

Uniform years have 12 months, 26 two-week intervals, 52 weeks or 365 days; no calendar dates or leap-day model. Inputs must be finite, nonnegative amounts and duration; the nominal period rate must exceed −100%. Finite results and interval counts up to the safe integer limit are supported; overflow or unrepresentable values are rejected. No taxes, fees, inflation or variable rates.

Context: Investor.gov compound interest calculator; deposit and crediting conventions are specified above.