APR ↔ APY Converter
Convert nominal annual percentage rate to effective annual yield.
Overview
The APR ↔ APY Converter translates a nominal annual percentage rate into an effective annual yield and back again. It's the calculator that tells you whether a 5% APR loan compounded monthly really costs 5% a year (it costs more) and whether a 4.9% APY savings account is better than a 5% APR one (it usually is).
Borrowers shopping mortgages, savers comparing high-yield accounts and finance students learning the time value of money all need to flip between APR and APY. Doing it by hand involves an exponent and a root — easy to fat-finger and easy to misinterpret.
How it works
APR is the nominal rate quoted before compounding. APY (also called effective annual rate or EAR) reflects the actual yearly return after compounding n times per year. The forward conversion is APY = (1 + APR / n)^n - 1. The inverse is APR = n * ((1 + APY)^(1/n) - 1).
When n goes to infinity the formula collapses to continuous compounding: APY = e^APR - 1 and APR = ln(1 + APY). Daily compounding (n = 365) is already very close to continuous for typical rates.
Examples
APR 5%, monthly compounding (n=12) → APY ≈ 5.1162%
APR 5%, daily compounding (n=365) → APY ≈ 5.1267%
APY 6%, monthly compounding → APR ≈ 5.8411%
APR 12%, continuous compounding → APY ≈ 12.7497%
FAQ
Which rate is more honest?
APY. It accounts for compounding so two products are directly comparable. Two loans with the same APR but different compounding schedules will have different APYs.
Why does daily compounding barely beat monthly?
Because compounding has diminishing returns. The gap from annual to monthly is the bulk of the effect; from monthly to daily is small; from daily to continuous is tiny.
Are credit-card APRs really APYs?
Most US credit cards quote APR with daily compounding, so the effective APY is slightly higher than the headline number — typically a few tenths of a percent.
What about fees?
This converter handles compounding only. For loans with origination fees or savings accounts with monthly maintenance fees, the realised return drops further.
Does it support negative rates?
Yes — useful for cases like negative-yielding bonds, though it is unusual in retail finance.