Question

Dr. Ruth is going to borrow $5,800 to help write a book. The loan is for one year and the money can be borrowed at either the prime rate or the LIBOR rate. Assume the prime rate is 9 percent and LIBOR 1.0 percent less. Also assume there will be a $55 transaction fee with LIBOR (this amount must be added to the interest cost with LIBOR). a. What is the effective interest rate on the LIBOR loan? (Use a 360-day year. Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.) b. Which loan has the lower effective interest cost? LIBOR Prime

Answer 1

Answer:

Ans.

a. The effective interest rate on the LIBOR loan is 8.95%

b. The loan with the lower effective rate is the LIBOR.

Explanation:

Hi, well, the Prime loan is pretty straight forward, the cost is 9%, on the other hand, the LIBOR loan requires some work. First, we have to find the future value of the loan, that is:

$FV=PresentValue+Interest+Fee$

That is:

$FutureValue=5,800+5,800*0.08+55=6,319$

In order to find the effective rate of the loan, and knowing that it is going to be paid one year from now, we need to use the following formula.

$r=\frac{FutureValue}{Present Value} -1$

$r=\frac{6,319}{5,800} -1=0.0895$

So, the cost of the LIBOR loan is 8.95% effective annual, and still lower than the PRIME loan.

Best of luck.