About this tool
APR ⇄ APY Converter is a free, in-browser tool that turns a nominal annual rate (APR) into its effective annual yield (APY), or the reverse. Pick which direction to solve, enter the rate, choose how often interest compounds, and the converted rate is computed instantly on your device.
With n compounding periods per year, APY = (1 + APR/n)^n − 1 and, going the other way, APR = n·((1 + APY)^(1/n) − 1). For continuous compounding the limits apply: APY = e^APR − 1 and APR = ln(1 + APY). The tool also shows the gap between the nominal and effective rates in percentage points, which is the extra return that compounding adds.
Use it to compare accounts and loans on equal footing — a 12% APR compounded monthly is really a 12.68% APY, so quoting one rate as if it were the other overstates or understates the true cost. More frequent compounding always widens the gap between APR and APY.
Frequently asked questions
What is the difference between APR and APY?
APR is the nominal annual rate that ignores in-year compounding, while APY (also called the effective annual rate) folds compounding in. For any positive rate the APY is at least as large as the APR, and they are equal only when interest compounds once a year.
How is continuous compounding handled?
As the number of periods grows without bound the formulas converge to the exponential limit: APY = e^APR − 1, and APR = ln(1 + APY). Select Continuous to use these instead of the discrete n-period formulas.
Why does a 12% APR become a 12.68% APY monthly?
Compounding monthly means (1 + 0.12/12)^12 − 1 = 0.1268, or 12.68%. Each month's interest itself earns interest for the rest of the year, so the effective yield ends up above the stated nominal rate.
Which rate should I compare between offers?
Compare APY to APY. Because APY already includes each product's compounding frequency, it is the apples-to-apples figure; comparing a monthly-compounded APR against an annually-compounded APR can be misleading.
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