Chapter 3: 15BP (page 250)

Randall Corporation plans to borrow $233,000 for one year at 20 percent from the Waco State Bank. There is a 21 percent compensating balance requirement. Randall Corporation keeps minimum transaction balances of $17,500 in the normal course of business. This idle cash counts toward meeting the compensating balance requirement. What is the effective rate of interest?

Short Answer

Expert verified

The effective interest rate is 23.11%.

Step by step solution

Information provided in the question

Loan amount = $233,000

Loan term = 1 year

Interest rate = 20%

Compensating balance = 21%

Minimum transaction balance = $17,500

Calculation of interest payable

The interest payable is $46,600.

$\begin{array}{rcl} Interest payable & = & Interest \times Principal \\ = & 20 % \times $ 233, 000 \\ = & $ 46, 600 \end{array}$

Calculation of compensating balance in monetary terms

The compensating balance is $48,930.

$\begin{array}{rcl} Compensating balance & = & Compensating balance rate \times Principal \\ = & 21 %\times$233,000 \\ = & $48,930 \end{array}$

Calculation of additional funds needed by the bank

The additional funds needed by the bank is $31,430.

$\begin{array}{rcl} Additional funds needed & = & Required compensating balance - Minimum transaction balance \\ = & $ 48, 930 - $ 17, 500 \\ = & $ 31, 430 \end{array}$

Calculation of effective interest rate on loan

The effective interest rate with a 21% compensating rate is 23.11%.

$\begin{array}{rcl} Effective rate & = & \frac{Interest}{Principal - Compensating balance} \times \frac{Days in year}{Days loan in outstanding} \\ = & \frac{$ 46, 600}{$ 233, 000 - $ 31, 430} \times \frac{360}{360} \\ = & 23.11 % \end{array}$

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January	\(28,000
February	\)19,000
March	\(12,000
April	\)14,000
May	\(8,000
June	\)6,000
July	\(22,000
August	\)26,000
September	\(29,000
October	\)34,000
November	\(42,000
December	\)24,000
Total annual sales	\(264,000

Short Answer

Step by step solution

Information provided in the question

Calculation of interest payable

Calculation of compensating balance in monetary terms

Calculation of additional funds needed by the bank

Calculation of effective interest rate on loan

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