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Equivalent Interest Rate Calculator

Equivalent Rate Calculator
I = 4.0133%

Rn (nominal) = 4%
Re (effective) = 4.0742%

In (nominal) = 4.0133%
Ie (effective) = 4.0742%

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Convert a nominal interest rate from one compounding frequency to another while keeping the effective interest rate constant.

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

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

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%

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

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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