APR vs APY Calculator
Convert a nominal APR to its effective APY at any compounding frequency and see what compounding adds.
How it works
APY = (1 + APR ÷ n)^n − 1 · Reverse: nominal = n × ((1 + APY)^(1 ÷ n) − 1)
APR is the stated annual rate before compounding; APY is what you actually earn or owe once interest compounds within the year. The more often it compounds, the larger the gap. Lenders often quote the lower APR, while banks advertise the higher APY on savings — knowing both lets you compare offers on the same footing.
Worked example
A 12% APR compounded monthly is (1 + 0.12 ÷ 12)^12 − 1 = 12.68% APY. That 0.68-point gap is purely the effect of compounding twelve times a year.
Frequently asked questions
Which is bigger, APR or APY?
APY is always at least as large as APR, and larger whenever interest compounds more than once a year. They are equal only with annual compounding.
Why do lenders quote APR but banks quote APY?
A lower advertised number looks better on a loan, so lenders show APR; a higher number looks better on savings, so banks show APY. Comparing like-for-like avoids being misled.
Does APR include fees?
For loans, APR often folds in certain fees on top of the interest rate, which is a separate adjustment from the compounding math shown here.
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This is an educational estimate, not financial advice. Confirm figures with your lender, advisor or tax professional.