Question

Dr. Ruth is going to borrow \(5,000 to help write a book. The loan is for one year and the money can either be borrowed at the prime rate or the LIBOR rate. Assume the prime rate is 11 percent and LIBOR 1.5 percent less. Also assume there will be a \)45 transaction fee with LIBOR (this amount must be added to the interest cost with LIBOR). Which loan has the lower effective interest cost?

Short answer

The LIBOR rate is less than the prime rate.

Step-by-step solution

Information provided in the question

Amount of loan = $5,000

Loan term = 1 year

Prime rate = 11%

LIBOR rate = 9.5%

Transaction fee in LIBOR = $45

Calculation of interest payable

The interest payable is $520.

$\begin{array}{rcl}\mathrm{Interest}\mathrm{payable}& =& \left(\mathrm{Interest}\mathrm{rate}\times \mathrm{Principal}\right)+\mathrm{Transaction}\mathrm{fee}\\ & =& \left(9.5\%\times \$5,000\right)+\$45\\ & =& \$520\end{array}$

Calculation of effective interest rate of LIBOR rate loan

The effective interest rate is 10.4%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{rate}& =& \frac{\mathrm{Interest}}{\mathrm{Principal}}\times \frac{\mathrm{Days}\mathrm{in}\mathrm{year}}{\mathrm{Days}\mathrm{loan}\mathrm{is}\mathrm{outstanding}}\\ & =& \frac{\$520}{\$5,000}\times \frac{360}{360}\\ & =& 10.4\%\end{array}$

Comparison between the prime rate and LIBOR interest rate

The prime rate is 11% and the effective LIBOR rate is 10.4%. Therefore, the LIBOR is lower than the prime rate, so this rate should be selected.