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Interest Rate Conversion

When interest on a loan is paid more than once in a year, the effective interest rate of the loan will be higher than the nominal or stated annual rate . For instance, if a loan carries interest rate of 8% p.a., payable semi annually, the effective annualized rate is 8.16% which is mathematically obtained by the conversion formula [(1+8%/2)^2-1]. We may, at times, need to compare an interest rate payable at certain frequency with interest rate payable at a different frequency. For instance, if there are two offers for a loan - one at an interest rate of 8% p.a. payable at half yearly intervals and the other at 7.9% p.a., but interest payable at monthly intervals; which one is advantageous in terms of effective annualized cost? Use Interest Rate Converter to compare such interest rates and to convert interest rate from one frequency to an equivalent of the rate payable in another frequency.

Interest Rate Conversion in Excel:

If you are interested in conversion formulae that can be used in Excel to convert interest rate from one frequency to an equivalent rate in another frequency, they are as follows: If 'Rate' is the interest rate:

From▼ \ To Monthly Quarterly H Yearly Annual
Monthly =((1+Rate/12)^1-1)*12 =((1+Rate/12)^3-1)*4 =((1+Rate/12)^6-1)*2 =((1+Rate/12)^12-1)*1
Quarterly =((1+Rate/4)^(1/3)-1)*12 =((1+Rate/4)^1-1)*4 =((1+Rate/4)^2-1)*2 =((1+Rate/4)^4-1)*1
Semi-Annual =((1+Rate/2)^(1/6)-1)*12 =((1+Rate/2)^(1/2)-1)*4 =((1+Rate/2)^(1/1)-1)*2 =((1+Rate/2)^2-1)*1
Annual =((1+Rate)^(1/12)-1)*12 =((1+Rate)^(1/4)-1)*4 =((1+Rate)^(1/2)-1)*2 =((1+Rate)^(1/1)-1)*1

You may extend the above logic further and attempt to derive the formulae for conversion of interest rate from other frequencies such such as weekly, daily, hourly etc into annualized rates as also into various other frequencies. The Rate Conversion Table spreadsheet demonstrates the use of the above formulas to convert interest rate from one frequency to another.

By the way, if interest (R) is compounded at infinite intervals (which is called as continuous compounding), what is the annualized equivalent of this rate? It can be computed in Excel by this function: =EXP(R)-1