Summit Record Company is negotiating with two banks for a \(151,000 loan. Fidelity Bank requires a 28 percent compensating balance, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a 14 percent compensating balance, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 10 percent. Compensating balances will be subtracted from the \)151,000 in determining the available funds in part a.

a. Calculate the effective interest rate for Fidelity Bank and Southwest Bank. Which loan should Summit accept?

Loan from fidelity bank:

Loan amount = $151,000

Instalments = Quarterly payments

Interest rate = 10%

Compensating balance = 28%

Loan from southwest bank:

Loan amount = $151,000

Instalments = Monthly payments

Interest rate = 10%

Compensating balance = 14%

The interest payable is $15,100.

$\begin{array}{rcl}\mathrm{Interest}\mathrm{payable}& =& \mathrm{Interest}\mathrm{rate}\times \mathrm{Principal}\\ & =& 10\%\times \$151,000\\ & =& \$15,100\end{array}$

The compensating balance is $42,280.

$\begin{array}{rcl}\mathrm{Compensating}\mathrm{balance}& =& \mathrm{Compensating}\mathrm{balance}\mathrm{rate}\times \mathrm{Principal}\\ & =& 28\%\times \$151,000\\ & =& \$42,280\end{array}$

The compensating balance is $21,140.

$\begin{array}{rcl}\mathrm{Compensating}\mathrm{balance}& =& \mathrm{Compensating}\mathrm{balance}\mathrm{rate}\times \mathrm{Principal}\\ & =& 14\%\times \$151,000\\ & =& \$21,140\end{array}$

The effective interest rate is 25.8%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{interest}\mathrm{rate}& =& \frac{2\times \mathrm{Annual}\mathrm{number}\mathrm{of}\mathrm{payments}\times \mathrm{Interest}\mathrm{rate}}{\left(\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{payments}+1\right)\times \left(\mathrm{Principal}-\mathrm{Interest}\mathrm{payable}-\mathrm{Compensating}\mathrm{balance}\right)}\\ & =& \frac{2\times 4\times \$15,100}{\left(4+1\right)\times \left(\$151,000-\$15,100-\$42,280\right)}\\ & =& \frac{\$120,800}{\$468,100}\\ & =& 25.8\%\end{array}$

The effective interest rate is 21.46%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{interest}\mathrm{rate}& =& \frac{2\times \mathrm{Annual}\mathrm{number}\mathrm{of}\mathrm{payments}\times \mathrm{Interest}\mathrm{rate}}{\left(\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{payments}+1\right)\times \left(\mathrm{Principal}-\mathrm{Compensating}\mathrm{balance}\right)}\\ & =& \frac{2\times 12\times \$15,100}{\left(12+1\right)\times \left(\$151,000-\$21,140\right)}\\ & =& \frac{\$362,400}{\$1,688,180}\\ & =& 21.46\%\end{array}$

The effective interest rate of Fidelity bank’s loan is 25.8% and Southwest bank’s loan is 21.46%. Summit record company should take the loan from Southwest bank.