Royal Company holds a loan with an interest rate of 8.00% compounded semi-annually. Calculate the effective rate of the loan.
Accepted Solution
A:
Effective Interest Rate = (1 + (Nominal Interest Rate / Number of Compounding Periods)) ^ Number of Compounding Periods - 1
In this case:
Nominal Interest Rate = 8.00% (0.08 as a decimal)
Number of Compounding Periods = 2 (semi-annually)
Plug these values into the formula:
Effective Interest Rate = (1 + (0.08 / 2))^2 - 1
Effective Interest Rate = (1 + 0.04)^2 - 1
Effective Interest Rate = (1.04)^2 - 1
Effective Interest Rate = 1.0816 - 1
Effective Interest Rate = 0.0816
To express the effective interest rate as a percentage, you can multiply by 100:
Effective Interest Rate = 0.0816 * 100% = 8.16%
So, the effective interest rate of the loan with an 8.00% nominal interest rate compounded semi-annually is approximately 8.16%.