APR to APY calculator

APR vs APY

The APR (annual percentage rate) is a nominal yearly rate: it does not include compounding. The APY (annual percentage yield) is what you actually earn in a year once interest is added to your balance and starts earning interest itself. The more often interest compounds, the higher the APY for the same APR. US banks must quote the APY on savings accounts and CDs under the Truth in Savings Act.

Formula

APY = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods per year.

Worked examples

A savings account paying 5% APR compounded monthly has an APY of 5.116%: each month you earn 0.4167%, and those monthly gains compound.

A 4.5% APR compounded daily is a 4.602% APY.

Going the other way, a 5% APY with monthly compounding corresponds to a 4.889% APR.

Comparing offers

Compare savings accounts by APY, since it already accounts for compounding. For loans, remember that a credit card's APR compounds too: a 24% APR card compounded daily costs about 27.1% a year.

To get the APY, the page divides the APR by the number of compounding periods per year, adds one, raises it to that number of periods and subtracts one. The reverse takes the n-th root of (1 + APY), subtracts one and multiplies by n. The periodic rate is the APR divided by n. Everything runs in your browser.