## 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.