Final answer:
The effective rate of interest when borrowing $20,000 at an annual interest rate of 23.5%, compounded semi-annually, is approximately 24.75%. There seems to be a slight error in the given answer options, but the closest choice is C. 24.25%.
Step-by-step explanation:
To find the effective rate of interest when borrowing $20,000 at an annual interest rate of 23.5%, compounded semi-annually, we need to use the formula for the effective annual rate (EAR):
EAR = (1 + i/n)n - 1
Where i is the nominal interest rate, and n is the number of compounding periods per year.
In this example, i is 23.5%, or 0.235, and n is 2 (since the interest compounds semi-annually).
EAR = (1 + 0.235/2)2 - 1
EAR = (1 + 0.1175)2 - 1
EAR = (1.1175)2 - 1
EAR = 1.11752 - 1
EAR = 1.24750625 - 1
EAR = 0.24750625
EAR = 24.750625%
After rounding to two decimal places, the effective rate of interest is approximately 24.75%, which is not one of the provided options. It seems there might be a slight error in the options, but the closest answer option would be C. 24.25%.