Question

The treasurer for the Macon Blue Sox baseball team is seeking a \(23,600 loan for one year from the 4th National Bank of Macon. The stated interest rate is 10 percent, and there is a 15 percent compensating balance requirement. The treasurer always keeps a minimum of \)2,280 in the baseball team’s checking accounts. These funds count toward meeting any compensating balance requirements. What will be the effective rate of interest on this loan?

Short answer

The effective interest rate is 10.56%.

Step-by-step solution

Information provided in the question

Loan amount = $23,600

Loan term = 1 year

Interest rate = 10%

Compensating balance = 15%

Minimum transaction balance = $2,280

Calculation of interest payable

The interest payable is $2,360.

$\begin{array}{rcl}\mathrm{Interest}\mathrm{payable}& =& \mathrm{Interest}\times \mathrm{Principal}\\ & =& 10\%\times \$23,600\\ & =& \$2,360\end{array}$

Calculation of compensating balance in monetary terms

The compensating balance is $3,540.

$\begin{array}{rcl}\mathrm{Compensating}\mathrm{balance}& =& \mathrm{Compensating}\mathrm{balance}\mathrm{rate}\times \mathrm{Principal}\\ & =& 15\%\times \$23,600\\ & =& \$3,540\end{array}$

Calculation of additional funds needed by the bank

The additional funds needed by the bank is $1,260.

$\begin{array}{rcl}\mathrm{Additional}\mathrm{funds}\mathrm{needed}& =& \mathrm{Required}\mathrm{compensating}\mathrm{balance}-\mathrm{Minimum}\mathrm{transaction}\mathrm{balance}\\ & =& \$3,540-\$2,280\\ & =& \$1,260\end{array}$

Calculation of effective interest rate on loan

The effective interest rate with a 15% compensating rate is 10.56%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{rate}& =& \frac{\mathrm{Interest}}{\mathrm{Principal}-\mathrm{Compensating}\mathrm{balance}}\times \frac{\mathrm{Days}\mathrm{in}\mathrm{year}}{\mathrm{Days}\mathrm{loan}\mathrm{is}\mathrm{outstanding}}\\ & =& \frac{\$2,360}{\$23,600-\$1,260}\times \frac{360}{360}\\ & =& 10.56\%\end{array}$