APR TO APY

APY Calculator

Convert a nominal APR to APY, or APY back to APR, with annual, semiannual, quarterly, monthly, daily, or continuous compounding.

Nominal APR and effective APY

APR here is the nominal annual rate divided across compounding periods. APY is the effective annual yield after that compounding. More frequent compounding raises APY when the nominal rate is positive. This is a compounding conversion, not a loan APR that folds in origination fees.

APY = (1 + APR ÷ n)^n − 1
APR = n × ((1 + APY)^(1 ÷ n) − 1)
Continuous APY = e^APR − 1
Continuous APR = ln(1 + APY)
Interest on $10,000 = $10,000 × APY

Example

A 5% APR compounded monthly is an APY of about 5.11619%. $10,000 left for one year at that APY earns about $511.62. Converting 5.11619% APY back with monthly compounding returns the 5% APR. Continuous compounding on 5% APR is about 5.12711% APY.

What this conversion leaves out

Account fees, teaser rates, tax, and a rate that changes during the year sit outside the formula. A loan APR with fees deducted at disbursement is a different cash-flow rate; use the loan APR calculator for that.

Frequently asked questions

Is APY always higher than APR?

When the nominal rate is positive and compounding is more than once a year, yes. At 0% they match. Continuous compounding is the upper limit for a given positive APR.

Does monthly compounding use 12 or 365/12?

This page uses 12 equal periods. Daily compounding uses 365 periods.

Is this the APR on a car loan or credit card?

No. Those products can use different day-count rules and fees. Enter only the nominal rate you want to convert.

Why show interest on $10,000?

It is a one-year illustration at the effective APY so the percentage is easier to compare. It is not a quoted account.

More calculators

Compound Interest Calculator →Simple Interest Calculator →Loan APR Calculator →

Calculations run in your browser. Values are not uploaded or stored.