# Effective Interest Rate Formula

## Formula

```Effective rate = (1 + i / m )n - 1
```
Where
i = Annual nominal rate of interest
m = Number of compounding periods in a year
n = Number of compounding periods the rate is required for

## Use

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

## Effective Interest Rate Formula Example 2

If the nominal rate is 9% compounded quarterly, what is the effective rate for a 6 month period?

The effective interest rate for the 6 month period is calculated using the effective rate formula as follows:

```Effective interest rate = (1 + i / m )n - 1
i = annual nominal rate = 9%
m = compounding periods in a year = 4
n = number of compounding periods the rate is required for = 2
Effective interest rate = (1 + 9% / 4 )2 - 1
Effective interest rate = 4.551% per six month period
```

## Effective Interest Rate Formula Example 2

If the nominal rate is 8% compounded monthly, what is the effective rate for one quarter?

The effective interest rate for the one quarter is calculated using the effective rate formula as follows:

```Effective interest rate = (1 + i / m )n - 1
i = annual nominal rate = 8%
m = compounding periods in a year = 12
n = number of compounding periods the rate is required for = 3 (one quarter)
Effective interest rate = (1 + 8% / 12 )3 - 1
Effective interest rate = 2.013% per quarter
```

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

Effective Interest Rate Formula November 6th, 2016