Chapter 3: 19BP (page 251)

Zerox Copying Company plans to borrow $172,000. New Jersey National Bank will lend the money at one-half percentage point over the prime rate at the time of 17½ percent (18 percent total) and requires a compensating balance of 21 percent. The principal in this case will be funds that the firm can effectively use in the business. This loan is for one year. What is the effective rate of interest? What would the effective rate be if Zerox were required to make four quarterly payments to retire the loan?

Short Answer

Expert verified

The effective interest rate is 22.78% and the effective interest rate on an instalment loan is 28.8%.

Step by step solution

Information provided in the question

Loan amount = $172,000

Loan term = 1 year

Interest rate = 18%

Compensating balance = 21%

Calculation of interest payable

The interest payable is $30,960.

$\begin{array}{rcl} Interest payable & = & Interest \times Principal \\ = & 18 % \times $ 172, 000 \\ = & $ 30, 960 \end{array}$

Calculation of compensating balance in monetary terms

The compensating balance is $36,120.

$\begin{array}{rcl} Compensating balance & = & Compensating balance rate \times Principal \\ = & 21 % \times $ 172, 000 \\ = & $ 36, 120 \end{array}$

Calculation of effective interest rate on loan

The effective interest rate with a 21% compensating rate is 22.78%.

$\begin{array}{rcl} Effective rate & = & \frac{Interest}{Principal - Compensating balance} \times \frac{Days in year}{Days loan is outstanding} \\ = & \frac{$ 30, 960}{$ 172, 000 - $ 36, 120} \times \frac{360}{360} \\ = & 22.78 % \end{array}$

Calculation of effective interest rate when quarterly instalments have to be made

The effective interest rate is 28.8%.

$\begin{array}{rcl} Effective rate on instalment & = & \frac{2 \times Annual number of payments \times Interest}{(Total number of payments + 1) \times Principal} \\ = & \frac{2 \times 4 \times $ 30, 960}{(4 + 1) \times $ 172, 000} \\ = & \frac{$ 247, 680}{$ 860, 000} \\ = & 28.8 % \end{array}$

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Short Answer

Step by step solution

Information provided in the question

Calculation of interest payable

Calculation of compensating balance in monetary terms

Calculation of effective interest rate on loan

Calculation of effective interest rate when quarterly instalments have to be made

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