APR to APY calculator

How it works

APR, annual percentage rate, is the stated yearly rate. APY, annual percentage yield, is what you actually earn over a year once the interest is compounded, meaning earned interest earns interest of its own. With APR r and n compounding periods a year:

APY = (1 + r ÷ n)ⁿ − 1

APR from APY = n × ((1 + APY)^{1 ÷ n} − 1)

The more often interest is compounded, the higher the APY, but with a limit: continuous compounding gives e^r − 1. The more important question for a quoted rate is not the compounding but whether it will be paid at all, and for how long.

Worked example

The page opens with 10% APR compounded daily. The APY is (1 + 0.10 ÷ 365)³⁶⁵ − 1 = 10.516%. Compounded monthly, the same 10% gives 10.471%. On 1,000 over one year, that is 1,105.16 at the end with daily compounding. Going the other way, an APY of 10.5% corresponds to an APR of 9.986% compounded daily.

APR and APY side by side

The gap between APR and APY is small at low rates and grows fast at high ones: a 100% APR compounded daily is a 171.46% APY. Compounding does not create the return. It only describes how the same stated rate is credited. To see what a yield minus costs leaves after many periods, use the compound growth calculator.

Questions

Which is higher, APR or APY?

APY is the same as APR or higher, and equal only when interest is compounded once a year. Platforms may quote the larger number because it looks better.

Is a quoted crypto yield guaranteed?

No. Variable rates change, many are paid in a token whose price can fall, and a platform can fail. Compounding arithmetic says nothing about those risks.

What does continuous compounding mean?

It is the limit of compounding more and more often. The factor is e raised to the APR. For a 10% APR it gives 10.517%, barely above daily compounding at 10.516%.

Why enter the number of years?

To see the amount at the end. The calculator compounds the APY, not the APR, for the whole period, which is equivalent.