FINANCEVELIX / Investment calculators
APR to APY and APY to APR converter
FINANCEVELIX / CRYPTO
Crypto tools
Convert a nominal annual rate (APR) into the effective yearly yield (APY) it produces, or work back from an APY to its APR. Choose how often interest or rewards compound, from once a year to continuously.
APR ↔ APY converter
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FINANCEVELIX / Method
How APR and APY are converted
APR is a nominal yearly rate that does not include compounding. APY, also called the effective annual rate, shows the yearly growth when interest is added to the balance and then earns interest itself. With n compounding periods a year: APY = (1 + APR ÷ n)^n − 1. For continuous compounding, APY = e^APR − 1.
Going the other way, APR = n × ((1 + APY)^(1 ÷ n) − 1), or ln(1 + APY) for continuous compounding. The rate per period is APR ÷ n.
Example: a 12% APR compounded monthly earns 1% a month, which grows to an APY of about 12.68%. Compounded daily, the same APR gives about 12.75%, and with annual compounding APR and APY are equal. The gap widens as the rate rises: a 100% APR compounded daily is an APY of about 171.46%.
In the United States, the Truth in Savings rules require banks to state deposit yields as APY. Crypto staking and lending platforms may show either figure, so check which one is quoted.
Frequently asked questions
What is the difference between APR and APY?
APR is the simple yearly rate before compounding, and APY is the effective yearly rate after compounding. They are equal only when interest compounds once a year. With more frequent compounding, a positive APY is higher than the APR.
Why do crypto platforms show such different APR and APY figures?
At high rates, compounding makes a large difference: a 50% APR compounded daily is an APY of about 64.82%. APY figures also assume rewards are reinvested every period at the same rate, which may not happen if rates change or rewards are paid out.
Is the APR on a loan the same as the rate I pay?
Not always. For loans, APR is the commonly quoted figure and, depending on local rules, can include certain fees. The effective rate including compounding, often called the effective annual rate (EAR), can be higher. Your loan agreement shows how interest is calculated.