Question

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

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.

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

Calculation of compensating balance in monetary terms

The compensating balance is $48,930.

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

Calculation of additional funds needed by the bank

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

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

Calculation of effective interest rate on loan

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

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