## 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.