# 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, 2016

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