Formula and 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 (m) a year. Additionally the rate is sometimes referred to as simply the effective rate.
The effective rate is the ‘real’ return that an investment makes when the effect of compounding over time is taken into account. This is in contrast to the nominal rate which takes no account of compounding.
Effective Interest Rate Formula Example 1
If the nominal rate is 9% compounded quarterly, what is the effective rate for a 6 month period?
The effective 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 Rate Increases with the Number of Compounding Periods
It can be shown that for a given term the effective interest rate increases as the number of compounding periods in a year (m) increases.
To illustrate suppose an amount is compounded at a nominal rate of 10% for a year. In the first case suppose the compounding is quarterly. The calculation of the effective rate is as follows.
Effective interest rate = (1 + i / m )n - 1 i = annual nominal rate = 10% m = compounding periods in a year = 4 (quarterly) n = number of compounding periods the rate is required for = 4 (one year) Effective interest rate = (1 + 10% / 4 )4 - 1 Effective interest rate = 10.381% per year
Next consider what happens if the amount is compounded monthly. In this case the calculation of the effective rate is as follows.
Effective interest rate = (1 + i / m )n - 1 i = annual nominal rate = 10% m = compounding periods in a year = 12 (monthly) n = number of compounding periods the rate is required for = 12 (one year) Effective interest rate = (1 + 10% / 12) 12 - 1 Effective interest rate = 10.471% per year
As can be seen for the given term (year), the effective rate is higher (10.471% compared to 10.381%) if the compounding period is more frequent (monthly compared to quarterly).
The effective rate formula is one of many used in time value of money calculations, discover another at the link below.
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 and has built financial models for 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 degree from Loughborough University.