What is the difference between APR and APY?

APR is the nominal annual rate and ignores compounding within the year. APY includes it. A nominal 12% compounded monthly is an APY of 12.68%, and deposits are advertised in APY while loans are advertised in APR, for reasons that flatter both.

Does more frequent compounding always mean more money?

Yes, but with a ceiling. Going from annual to monthly on a nominal 12% adds 0.68 points; going from monthly to continuous adds a further 0.07. There is no arrangement of compounding that beats e^r - 1.

Finance & LoanssavingsUnited States only

APY Calculator

APR to APY. Savings products quote APY and loans quote APR, and comparing the two directly is comparing different things.

Also called: annual percentage yield calculator, apy vs apr.

APY

5.13%

An APR of 5% compounded 365 times a year is an APY of 5.13%.

Difference

0.13%

How this is calculated

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

Identical mathematics to the effective annual rate. The naming difference is regulatory rather than mathematical: deposits must be advertised as APY because it is the larger, more honest number for a saver, and loans as APR.

apy = (1 + apr/m)^m - 1

m: Compounding periods per year

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

5% daily compounded

APR (nominal rate): 5%
Compounded: Daily

APY5.13%

(1 + 0.05/365)^365 - 1

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annual compounding is the identity

APR (nominal rate): 5%
Compounded: Annually

APY5%

degenerate case

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zero rate

APR (nominal rate): 0%
Compounded: Daily

APY0%

boundary

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Frequently asked questions

What is the difference between APR and APY?: APR is the nominal annual rate and ignores compounding within the year. APY includes it. A nominal 12% compounded monthly is an APY of 12.68%, and deposits are advertised in APY while loans are advertised in APR, for reasons that flatter both.
Does more frequent compounding always mean more money?: Yes, but with a ceiling. Going from annual to monthly on a nominal 12% adds 0.68 points; going from monthly to continuous adds a further 0.07. There is no arrangement of compounding that beats e^r - 1.