Finance / Interest
APR to APY Calculator (Effective Annual Rate)
Convert a nominal annual percentage rate (APR) to the annual percentage yield (APY, the effective annual rate) for yearly, monthly, daily, or continuous compounding, or convert an APY back to its APR.
APR to APY Calculator (Effective Annual Rate): Interest compounded n times a year at a nominal APR earns APY = (1 + APR ÷ n)^n − 1 over the year, because each period's interest earns interest too; continuous compounding gives e^APR − 1. A 5% APR compounded monthly is an APY of 5.116%, and daily 5.127%. The reverse formula, APR = n × ((1 + APY)^(1/n) − 1), turns a quoted APY back into its nominal rate. Runs 100% locally in your browser with zero server file uploads.
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APR is the nominal yearly rate before compounding; APY, also called the effective annual rate (EAR or AER), includes the interest earned on interest. APY = (1 + APR ÷ n)^n − 1 for n compounding periods a year, or e^APR − 1 for continuous compounding. Savings accounts usually quote APY; loans often quote APR, which in some countries also includes fees.
Worked examples
A savings account at 4.5% APR compounded monthly yields 4.594% APY. A credit card at 24% APR compounded daily costs an effective 27.1% a year if the balance is carried.
To see the growth over several years, use the compound interest calculator.
Names for the same idea
APY is called the annual equivalent rate (AER) in the UK, the effective annual rate (EAR) in finance texts, and TAE (tasa anual equivalente) in Spain; Europe's TAEG for loans includes costs as well as interest.
For the value of money at different points in time, see the present and future value calculator.
How to use it
- Choose APR to APY or APY to APR.
- Enter the rate and choose how often interest compounds.
- Read the converted rate and what it means on 10,000 over a year.
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Frequently asked questions
Which is higher, APR or APY?
APY, whenever interest compounds more than once a year; they are equal for yearly compounding.
Which should I compare?
Compare APYs for savings, because they include compounding. For loans, compare the APR the lender is required to quote, which in some countries includes fees as well.
Does daily compounding make a big difference?
Not much over monthly: at 5%, monthly gives 5.116% and daily 5.127%.
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