Equivalent Interest Rate Calculator

Equivalent Rate Calculator
Interest Rate per Period (R)
Compounding per Period (m)
New Compounding per Period (q)

I = 4.0133%

R (nominal) = 4%
R (effective) = 4.0742%
rate per period m = 0.3333%

I (nominal) = 4.0133%
I (effective) = 4.0742%
rate per period q = 1.0033%

Calculator Use

Convert an interest rate from one compounding frequency to another.

Given the periodic nominal rate r compounded m times per per period, the equivalent periodic nominal rate i compounded q times per period is

\[ i = q\times\left[\left(1+\frac{r}{m}\right)^{m/q}-1\right] \]

where r = R/100 and i = I/100.

For example, you have a loan at an annual rate of 4% that compounds monthly (m=12) however your payments are made quarterly (q=4) so your interest will be calculated quarterly.  What is the equivalent annual rate that coincides with quarterly compounding? 4.0133%

\[ i\,=\,4\times\left[\left(1+\frac{0.04}{12}\right)^{12/4}-1\right]\,=\,0.040133 \]

The effective annual interest rate remains the same.


Cite this content, page or calculator as:

Furey, Edward "Equivalent Interest Rate Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.

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