If nominal interest rate is 12% and it is compounded monthly, what is the effective interest rate per interest period?
Question
If nominal interest rate is 12% and it is compounded monthly, what is the effective interest rate per interest period?
Solution
To calculate the effective interest rate per interest period when the nominal interest rate is 12% and it is compounded monthly, you can use the formula for the effective annual rate (EAR):
EAR = (1 + i/n)^(nt) - 1
where: i = nominal interest rate = 12% = 0.12 n = number of compounding periods per year = 12 (monthly compounding) t = number of years = 1 (since we're looking for the annual rate)
Substituting the values into the formula, we get:
EAR = (1 + 0.12/12)^(12*1) - 1
Solving this step by step:
- Calculate the value inside the brackets: 1 + 0.12/12 = 1.01
- Raise this value to the power of 12: 1.01^12 ≈ 1.126825
- Subtract 1 from the result: 1.126825 - 1 = 0.126825
So, the effective interest rate per interest period (i.e., per month) is approximately 12.68%.
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