Question

Dr. Ruth is going to borrow $6,000 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 11 percent and LIBOR 2.5 percent less. Also assume there will be a $70 transaction fee with LIBOR (this amount must be added to the interest cost with LIBOR).

What is the effective interest rate on the LIBOR loan?
Note: 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?

I guessed LIBOR and got it correct.

Answer 1

To calculate the effective interest rate on the LIBOR loan, we first need to calculate the LIBOR rate, which is 2.5% less than the prime rate:

LIBOR rate = prime rate - 2.5% = 11% - 2.5% = 8.5%

Next, we need to calculate the interest cost of the LIBOR loan, taking into account the transaction fee:

Interest cost = (loan amount x LIBOR rate x loan period) + transaction fee
Interest cost = ($6,000 x 8.5% x 1 year) + $70
Interest cost = $510 + $70
Interest cost = $580

The effective interest rate is calculated by dividing the total interest cost by the loan amount and expressing the result as a percentage:

Effective interest rate = (total interest cost / loan amount) x (360 / loan period)
Effective interest rate = ($580 / $6,000) x (360 / 1)
Effective interest rate = 9.67%

Therefore, the effective interest rate on the LIBOR loan is 9.67%.

To determine which loan has the lower effective interest cost, we need to calculate the interest cost and effective interest rate for the prime rate loan:

Interest cost = (loan amount x prime rate x loan period) = ($6,000 x 11% x 1 year) = $660
Effective interest rate = (total interest cost / loan amount) x (360 / loan period) = ($660 / $6,000) x (360 / 1) = 11.00%

The LIBOR loan has a lower effective interest cost (9.67% vs. 11.00%), so it is the better option.