Chapter 3: 14BP (page 250)

Carey Company is borrowing $200,000 for one year at 12 percent from Second Intrastate Bank. The bank requires a 20 percent compensating balance. What is the effective rate of interest? What would the effective rate be if Carey were required to make 12 equal monthly payments to retire the loan? The principal, as used in Formula 8-6, refers to funds the firm can effectively utilize (Amount borrowed - Compensating balance).

Short Answer

Expert verified

The effective interest rate is 15% and the effective interest rate on an instalment loan is 22.15%.

Step by step solution

Information provided in the question

Loan amount = $200,000

Loan term = 1 year

Interest rate = 12%

Compensating balance = 20%

Calculation of interest payable

The interest payable is $24,000.

$\begin{array}{rcl} Interest payable & = & Interest \times Principal \\ = & 12 % \times $ 200, 000 \\ = & $ 24, 000 \end{array}$

Calculation of compensating balance in monetary terms

The compensating balance is $40,000.

$\begin{array}{rcl} Compensating balance & = & Compensating balance rate \times Principal \\ = & 20 % \times $ 200, 000 \\ = & $ 40, 000 \end{array}$

Calculation of effective interest rate on the loan

The effective interest rate with a 20% compensating rate is 15%.

$\begin{array}{rcl} Effective rate & = & \frac{Interest}{Principal - Compensating balance} \times \frac{Days in year}{Days loan is outstanding} \\ = & \frac{$ 24, 000}{$ 200, 000 - $ 40, 000} \times \frac{360}{360} \\ = & 15 % \end{array}$

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

The effective interest rate is 22.15%.

$\begin{array}{rcl} Effective rate on instalment loan & = & \frac{2 \times Annual number of payment \times Interest}{(Total number of payments + 1) \times Principal} \\ = & \frac{2 \times 12 \times $ 24, 000}{(12 + 1) \times $ 200, 000} \\ = & \frac{$ 576, 000}{$ 2, 600, 000} \\ = & 22.15 % \end{array}$

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January	\(65,000
February	\)55,000
March	\(100,000
April	\)45,000

Age of receivables April 30 20X1
1	2	3	4
Month of sales	Age of accounts	Amounts	Percent of amount due
April	0-30	\(131,250	____
March	31-60	\)93,750	____
February	61-90	\(112,500	____
January	91-120	\)37,500	____
Total receivables		$375,000	100%

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 the loan

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

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