Effective Annual Rate Formula

Formula

EAR = (1 + i / m )m - 1
Where
i = Annual nominal rate of interest
m = Number of compounding periods in a year

Use

The effective annual rate formula calculates the rate of interest for a year based on a nominal rate (i) compounded a number of times a year (m).

The effective annual rate is sometimes abbreviated to EAR and often referred to as the annual equivalent rate or AER.

Excel Function

The Excel EFFECT function can be used instead of the effective annual rate formula, and has the syntax shown below.

EFFECT(i,m)

Effective Annual Rate Formula Example

If the nominal rate is 9% compounded quarterly, what is the effective annual rate?

The effective interest rate for the year is calculated using the effective annual rate formula as follows:

Effective annual rate = (1 + i / m )m - 1
i = annual nominal rate = 9%
m = compounding periods in a year = 4
Effective annual rate = (1 + 9% / 4 )4 - 1
Effective annual rate = 9.308%

The same answer can be obtained using the Excel EFFECT function as follows:

Effective annual rate = EFFECT(i,m)
i = 9%
m = 4 
Effective annual rate = EFFECT(9%, 4)
Effective annual rate = 9.308%

The effective annual rate formula is one of many used in time value of money calculations, discover another at the links below.

Effective Annual Rate Formula November 6th, 2016Team

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