Effective Annual Rate Calculator
Convert between a nominal annual interest rate (APR) and the effective annual rate (EAR, also called APY or annual percentage yield) for a given compounding frequency. The nominal rate is the per-year rate before compounding; the effective rate is what you actually earn or pay once compounding is included. Choose a compounding frequency (annual, semiannual, quarterly, monthly, weekly, daily, continuous, or a custom number of periods per year), then enter either the nominal rate to get the EAR or the EAR to back out the nominal rate. The periodic rate is shown too. Everything runs locally in your browser.
EAR = (1 + r/n)^n − 1 for n periods per year and nominal rate r; for continuous compounding EAR = e^r − 1. To invert, r = n·((1 + EAR)^(1/n) − 1), or r = ln(1 + EAR) for continuous. The periodic rate is r/n (or e^(r/n)−1 per period for continuous — here we report the nominal periodic rate r/n). APR/APY differ because APR is the nominal rate and APY is the effective rate after compounding; U.S. truth-in-lending uses APR for loans and APY for deposits. Runs locally.