An annual interest rate of 12% compounded monthly has an effective yield of? 7. An annual interest rate of 12% compounded quarterly has an effective yield of? 8. A simple annual interest rate of 12% compounded semi-annually is an effective yield of?
Question
An annual interest rate of 12% compounded monthly has an effective yield of? 7. An annual interest rate of 12% compounded quarterly has an effective yield of? 8. A simple annual interest rate of 12% compounded semi-annually is an effective yield of?
Solution
- An annual interest rate of 12% compounded monthly:
The formula for the effective annual rate (EAR) is: EAR = (1 + i/n)^(nt) - 1
Where: i = nominal interest rate (12% or 0.12 in this case) n = number of compounding periods per year (12 for monthly compounding) t = number of years (1 in this case)
So, EAR = (1 + 0.12/12)^(12*1) - 1 = 0.126825 or 12.6825%
- An annual interest rate of 12% compounded quarterly:
Here, n = 4 for quarterly compounding.
So, EAR = (1 + 0.12/4)^(4*1) - 1 = 0.125509 or 12.5509%
- A simple annual interest rate of 12% compounded semi-annually:
Here, n = 2 for semi-annual compounding.
So, EAR = (1 + 0.12/2)^(2*1) - 1 = 0.1236 or 12.36%
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