Question

Carey Company is borrowing $200,000 for one year at 12 percent from Second Intrastate Bank. The bank requires a 20 percent compensating balance. What is the effective rate of interest? What would the effective rate be if Carey were required to make 12 equal monthly payments to retire the loan? The principal, as used in Formula 8-6, refers to funds the firm can effectively utilize (Amount borrowed - Compensating balance).

Short answer

The effective interest rate is 15% and the effective interest rate on an instalment loan is 22.15%.

Step-by-step solution

Information provided in the question

Loan amount = $200,000

Loan term = 1 year

Interest rate = 12%

Compensating balance = 20%

Calculation of interest payable

The interest payable is $24,000.

$\begin{array}{rcl}\mathrm{Interest}\mathrm{payable}& =& \mathrm{Interest}\times \mathrm{Principal}\\ & =& 12\%\times \$200,000\\ & =& \$24,000\end{array}$

Calculation of compensating balance in monetary terms

The compensating balance is $40,000.

$\begin{array}{rcl}\mathrm{Compensating}\mathrm{balance}& =& \mathrm{Compensating}\mathrm{balance}\mathrm{rate}\times \mathrm{Principal}\\ & =& 20\%\times \$200,000\\ & =& \$40,000\end{array}$

Calculation of effective interest rate on the loan

The effective interest rate with a 20% compensating rate is 15%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{rate}& =& \frac{\mathrm{Interest}}{\mathrm{Principal}-\mathrm{Compensating}\mathrm{balance}}\times \frac{\mathrm{Days}\mathrm{in}\mathrm{year}}{\mathrm{Days}\mathrm{loan}\mathrm{is}\mathrm{outstanding}}\\ & =& \frac{\$24,000}{\$200,000-\$40,000}\times \frac{360}{360}\\ & =& 15\%\end{array}$

Calculation of effective interest rate when equal instalments have to be made

The effective interest rate is 22.15%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{rate}\mathrm{on}\mathrm{instalment}\mathrm{loan}& =& \frac{2\times \mathrm{Annual}\mathrm{number}\mathrm{of}\mathrm{payment}\times \mathrm{Interest}}{\left(\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{payments}+1\right)\times \mathrm{Principal}}\\ & =& \frac{2\times 12\times \$24,000}{\left(12+1\right)\times \$200,000}\\ & =& \frac{\$576,000}{\$2,600,000}\\ & =& 22.15\%\end{array}$