APR Desk
APR Desk · APR and APY

APR to APY converter

Nominal rate and effective annual yield

APR to APY conversion answers a labeling problem. A nominal APR quotes the rate before compounding. An APY, or effective annual yield, quotes what a year of compounding actually produces. The same nominal rate yields more when it compounds more often. This page converts in either direction once you say how many times a year the rate compounds.

Inputs

Result

Enter a rate and how often it compounds.

Disclaimer: A rate conversion, not a savings offer or a loan disclosure. Use the compounding frequency your account or note actually uses.

Growing a deposit for several years, not just renaming the rate, is the compound interest calculator.

How to use

  1. Choose APR to APY if you have a nominal rate, or APY to APR if you have an effective annual yield and want the nominal quote.
  2. Enter the rate as a percent. Twelve means 12 percent, not 0.12.
  3. Set how many times the rate compounds in a year. Monthly is 12. Daily here means 365.
  4. Press Calculate. Both the APR and the APY are shown so you can check the direction.

How it's calculated

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

n is the number of compounding periods per year. If n is 1, APR and APY are the same number, because nothing compounds inside the year. As n rises, the APY of a given APR rises, but it does not rise without limit. The page does not use continuous compounding (e^APR − 1). If you need a balance over several years, take the APY or the nominal rate to the compound interest calculator.

A loan payment uses the nominal monthly rate APR ÷ 12. It does not substitute the APY. Mixing them double-counts compounding. The loan payoff calculator expects the APR you want divided by 12.

Worked example

A 12 percent APR compounded monthly is (1 + 0.12 ÷ 12)^12 − 1 = (1.01)^12 − 1 = 12.6825 percent APY. The same 12 percent compounded once a year is a 12 percent APY. Going backward, a 12.6825 percent APY with monthly compounding returns a 12 percent APR.

Assumptions and sources

The identities are the definitions of effective annual rate and nominal rate under periodic compounding, as used in standard finance references. They assume every period has an equal rate of APR ÷ n and that the quoted APR is not already an effective rate. Truth in Lending disclosures have their own APR rules for loans; this page is the mathematical conversion, not a reproduction of a disclosure form.

FAQ

Why is APY higher than APR?

APY includes compounding within the year. APR, in the nominal sense used here, does not. If the rate compounds only once a year, they match.

What number do I use for a loan payment?

Use the nominal APR divided by 12 as the monthly rate. Do not plug the APY into the loan formula.

Does daily mean 365 or 360?

This converter uses 365 when you pick daily. Some contracts use 360. If yours does, the result will not match the contract.

Can I convert a rate that compounds weekly?

The menu has the common frequencies. Weekly is 52, which is not in the menu; the formulas on the page are enough to do that case by hand.

Related tools