Question $4$

A construction company is taking out a $$17,000$ loan with an annual percentage rate of $11\%,$ compounded monthly, for a term of five years to finance the purchase of new equipment. The bank charges $$500$ in closing costs, which cannot be added to the $$17,000$ loan amount.

$$

a$)$ What effect do the closing costs have on the effective annual interest rate for the loan?

b$)$ If the company pays off the loan at the end of the thirtieth month $($at the time of the $30$th payment$),$ what impact does this have on the effective annual interest rate?

c$)$ Reflecting on your calculations for parts $($a$)$ and $($b$),$ identify any potential mistakes or challenges you encountered during the calculations. How did you verify the accuracy of your results, and what steps did you take to ensure the calculations were correct?