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.

Last modified November 6th, 2016 by Michael Brown

About the Author

Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years in all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.

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