Compound interest earns returns on both the original principal and the accumulated interest — giving each period's interest its own interest in subsequent periods. Over long time horizons, this creates exponential growth that linear interest cannot match. The formula: FV = P × (1 + r/n)^(n×t), where P is principal, r is annual rate, n is compounds per year, and t is years.
The more frequently interest compounds, the more you earn — but the difference shrinks as frequency increases. £10,000 at 5% for 10 years: annual compounding gives £16,288; monthly compounding gives £16,470; daily gives £16,487. The difference between monthly and daily is only £17 — far less meaningful than the rate itself or the time horizon. The limit as compounding frequency approaches infinity is continuous compounding: FV = P × e^(r×t).
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in approximately 72/6 = 12 years. It is a useful mental shortcut for comparing investment rates.
APR (Annual Percentage Rate) is the stated interest rate before compounding. APY (Annual Percentage Yield) is the effective rate after compounding is applied. For a 6% APR compounded monthly, the APY is (1 + 0.06/12)^12 − 1 ≈ 6.17%.
Compounding at every infinitesimally small interval — the mathematical limit as n approaches infinity. The formula is FV = P × e^(rt). It gives slightly higher returns than daily compounding but is mainly used in financial modelling and option pricing.
Yes — enable the regular contributions field and enter a monthly or annual amount. The tool adds each contribution with compounding from the date it is made, giving an accurate future value for a savings plan.
See also the Currency Converter, Discount Calculator, and VAT Calculator.