Convert Between Interest Rates with Different Compounding Frequencies

Learn how to convert between interest rates with different compounding frequencies.

Many financial products accrue interest at different rates.

For example, savings accounts offered by different banks may not have the same compounding frequency. Additionally, mortgages offered in some countries accrue interest once per year, while other countries have higher compounding frequencies.

Assume that you have an interest rate of r1, invested for T years and a compounding frequency of f1 times per year. The total amount accrued after T years is

Equation for the amount accrued under an investment at an interest rate with a compounding frequencyLets say that you want to calculate the equivalent interest rate for a compounding frequency of f2. The amount accrued under the new compounding frequency is

eq2

However, G1 = G2, and hence

eq3Rearranging this equation gives a formula for r2

Conversion formula between interest rates with different compounding frequenciesNote that r2 has no dependence on the investment time T.

Excel spreadsheet to convert between interest rates with different compounding frequencies

This Excel spreadsheet will let you experiment with the concepts in this article.

Consider an annual interest rate of 10% with an annual compounding frequency (i.e. once per year). The equivalent interest rate for a quarterly compounding frequency is 9.65%.

You may notice that higher compounding frequencies result in lower interest rates.

Excel Tool to Convert Between Interest Rates with Different Compounding Frequencies


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