Chapter 3: 17BP_d (page 251)

Your company plans to borrow $13 million for 12 months, and your banker gives you a stated rate of 24 percent interest. You would like to know the effective rate of interest for the following types of loans. (Each of the following parts stands alone.)
d. Discounted interest with a 5 percent compensating balance.

Short Answer

Expert verified

The effective interest rate is 1.84%.

Step by step solution

Information provided in the question

Loan amount = $13,000,000

Loan term = 1 year

Interest rate = 24%

Compensating balance = 5%

Calculation of interest payable

The interest payable is $3,120,000.

$\begin{array}{rcl} Interest payable & = & Interest \times Principal \\ = & 24 % \times $ 13, 000, 000 \\ = & $ 3, 120, 000 \end{array}$

Calculation of compensating balance

The compensating balance is $650,000.

$\begin{array}{rcl} Compensating balance & = & Compensating balance rate \times Principal \\ = & 5 % \times $ 13, 000, 000 \\ = & $ 650, 000 \end{array}$

Calculation of effective interest rate

The effective interest rate with a compensating balance of 5% is 1.84%.

$\begin{array}{rcl} Effective rate & = & \frac{Interest}{Principal - Interest - Compensating balance} \times \frac{Days in a year}{Days loan is outstanding} \\ = & \frac{$ 3, 120, 000}{$ 13, 000, 000 - $ 3, 120, 000 - $ 650, 000} \times \frac{360}{360} \\ = & \frac{$ 3, 120, 000}{$ 169, 000, 000} \times 1 \\ = & 1.84 % \end{array}$

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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 compensating balance

Calculation of effective interest rate

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