What does the effective annual rate tell me that the nominal rate does not?

What a year actually costs or pays once compounding within the year is included. It is the only figure on which two products with different compounding frequencies can be compared honestly.

Is the effective rate the same as APY?

Yes for deposits. The terms are used in different markets for the same arithmetic, with APY the usual label in US retail banking and effective annual rate the usual one in finance.

Finance & Loansloans

Effective Annual Rate Calculator

The one number that makes two differently-compounded rates comparable. This is the whole content of the APR-versus-APY question.

Also called: ear calculator, effective rate from nominal.

Effective annual rate

10.47%

A nominal 10% compounded 12 times a year is an effective 10.47%. 0.47% percentage points more than the headline.

Difference from the nominal rate

0.47%

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

Compounding more often on the same nominal rate earns more, because interest starts earning interest sooner. EAR expresses that as a single annual figure, which is why a savings product quoting APY and a loan quoting nominal APR cannot be compared without converting one of them.

ear = (1 + r/m)^m - 1

r: Nominal annual rate (decimal)
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.

10% monthly is 10.4713%

Nominal annual rate: 10%
Compounded: Monthly

Effective annual rate10.47%

DRV-003 worked example

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continuous is e^r - 1

Nominal annual rate: 10%
Compounded: Continuously

Effective annual rate10.52%

DRV-003 limit: e^0.1 - 1

Open this example

annual compounding changes nothing

Nominal annual rate: 10%
Compounded: Annually

Effective annual rate10%

degenerate case: m=1 is the identity

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Frequently asked questions

What does the effective annual rate tell me that the nominal rate does not?: What a year actually costs or pays once compounding within the year is included. It is the only figure on which two products with different compounding frequencies can be compared honestly.
Is the effective rate the same as APY?: Yes for deposits. The terms are used in different markets for the same arithmetic, with APY the usual label in US retail banking and effective annual rate the usual one in finance.