APY vs APR calculator

Enter a nominal annual rate and how often it compounds to get the effective annual yield (APY) and the extra interest compounding produces.

How this calculator works

APR and APY both describe an annual rate, but they count compounding differently. APR is the nominal rate — the number a bank quotes before compounding. APY, also called the effective annual rate, includes the effect of interest being added to the balance during the year and compounding. For the same nominal APR, more frequent compounding gives a higher APY.

The gap is tiny at low rates and grows with the rate: 5% compounded daily is 5.13% APY, while 20% compounded daily is 22.13% APY. That is why comparing savings accounts and loans on APY rather than APR is fairer — APY is what you actually earn or pay over a year. Note that banks may quote a daily rate without compounding; this calculator assumes the quoted rate compounds at the selected frequency, which is the standard APY definition.

The formula

For nominal annual rate a (as a decimal) compounded n times a year:

The interest earned on balance P is P × APY. The rate for each compounding period is a / n. In the limit of continuous compounding, APY becomes e^a − 1.

Worked example

A nominal 5% rate compounded monthly has an effective annual rate of 5.12%. On a 10,000 balance that is $511.62 of interest in the year — $11.62 more than the nominal rate would suggest.

Common mistakes

• Comparing APR on a savings account with APY. The APY always looks slightly higher because it includes compounding. Compare like with like.
• Assuming APR is the true cost of a loan. For loans, APR includes most fees, so it is usually higher than the interest rate but lower than the rate you actually pay if you pay early or make minimum payments.
• Ignoring compounding frequency in long-term projections. The difference compounds too: over 30 years, monthly versus annual compounding is worth several percent of the final balance.