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
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