Chapter 3: 8BP (page 249)

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

Expert verified

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

Calculation of effective interest rate of LIBOR rate loan

The effective interest rate is 10.4%.

$\begin{array}{rcl} Effective rate & = & \frac{Interest}{Principal} \times \frac{Days in year}{Days loan is outstanding} \\ = & \frac{$ 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.

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January	\(100,000
February	\)93,000
March	\(25,000
April	\)25,000
May	\(20,000
June	\)35,000
July	\(45,000
August	\)45,000
September	\(55,000
October	\)85,000
November	\(105,000
December	\)123,000
Total annual sales	\(756,000

Short Answer

Step by step solution

Information provided in the question

Calculation of interest payable

Calculation of effective interest rate of LIBOR rate loan

Comparison between the prime rate and LIBOR interest rate

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