Question

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

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.

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

Calculation of compensating balance

The compensating balance is $650,000.

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

Calculation of effective interest rate

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

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