Question

Maxim Air Filters Inc. plans to borrow $300,000 for one year. Northeast National Bank will lend the money at 10 percent interest and requires a compensating of 20 percent. What is the effective rate of interest?

Short answer

The effective interest rate is 12.5%.

Step-by-step solution

Information provided in the question

Loan amount = $300,000

Loan term = 1 year

Interest rate = 10%

Compensating rate = 20%

Calculation of interest payable

The interest payable is $30,000.

$\begin{array}{rcl}\mathrm{Interest}\mathrm{payable}& =& \mathrm{Interest}\times \mathrm{Principal}\\ & =& 10\%\times \$300,000\\ & =& \$30,000\end{array}$

Calculation of compensating balance in monetary terms

The compensating balance is $60,000.

$\begin{array}{rcl}\mathrm{Compensating}\mathrm{balance}& =& \mathrm{Rate}\times \mathrm{Principal}\\ & =& 20\%\times \$300,000\\ & =& \$60,000\end{array}$

Calculation of effective interest rate on loan

The effective interest rate with a 20% compensating rate is 12.5%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{rate}& =& \frac{\mathrm{Interest}}{\mathrm{Principal}-\mathrm{Compensating}\mathrm{balance}}\times \frac{\mathrm{Days}\mathrm{in}\mathrm{year}}{\mathrm{Days}\mathrm{loan}\mathrm{is}\mathrm{outstanding}}\\ & =& \frac{\$30,000}{\$300,000-\$60,000}\times \frac{360}{360}\\ & =& 12.5\%\end{array}$