Nominal and effective interest ratesBeing able to calculate an effective rate from a nominal rate and vice versa is a critical skillYou are quoted a rate of 6% on a mortgage. What is the effective annual rate based on semiannual compounding?6.09%5.83%3.00%5.91%
Question
Nominal and effective interest ratesBeing able to calculate an effective rate from a nominal rate and vice versa is a critical skillYou are quoted a rate of 6% on a mortgage. What is the effective annual rate based on semiannual compounding?6.09%5.83%3.00%5.91%
Solution
To calculate the effective annual rate (EAR) based on semiannual compounding, you can use the following formula:
EAR = (1 + i/n)^(nt) - 1
where: i = nominal interest rate n = number of compounding periods per year t = number of years
In this case, the nominal interest rate (i) is 6% or 0.06 (expressed as a decimal), the number of compounding periods per year (n) is 2 (since it's semiannual), and the number of years (t) is 1 (since we're looking for the annual rate).
So, the calculation would be:
EAR = (1 + 0.06/2)^(2*1) - 1 EAR = (1 + 0.03)^2 - 1 EAR = 1.0609 - 1 EAR = 0.0609 or 6.09%
So, the effective annual rate based on semiannual compounding is 6.09%.
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