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.

b. Recompute the effective cost of interest, assuming that Summit ordinarily maintains $42,280 at each bank in deposits that will serve as compensating balances.

Loan from fidelity bank:

Loan amount = $151,000

Instalments = Quarterly payments

Interest rate = 10%

Compensating balance = $42,280

Loan from southwest bank:

Loan amount = $151,000

Instalments = Monthly payments

Interest rate = 10%

Compensating balance = $42,280

The interest payable is $15,100.

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

The effective interest rate is 31.83%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{interest}\mathrm{rate}& =& \frac{2\times \mathrm{Annual}\mathrm{number}\mathrm{of}\mathrm{payments}\times \mathrm{Interest}\mathrm{rate}}{\left(\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{payments}+1\right)\times \left(\mathrm{Principal}-\mathrm{Interest}\mathrm{payable}\right)}\\ & =& \frac{2\times 4\times \$15,100}{\left(4+1\right)\times \left(\$151,000-\$15,100\right)}\\ & =& \frac{\$120,800}{\$379,500}\\ & =& 31.83\%\end{array}$

The effective interest rate is 1.46%.

$\begin{array}{rcl}\mathrm{Effective}\mathrm{interest}\mathrm{rate}& =& \frac{2\times \mathrm{Annual}\mathrm{number}\mathrm{of}\mathrm{payments}\times \mathrm{Interest}\mathrm{rate}}{\left(\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{payments}+1\right)\times \mathrm{Principal}}\\ & =& \frac{2\times 12\times \$15,100}{\left(12+1\right)\times \$151,000}\\ & =& \frac{\$362,400}{\$1,963,000}\\ & =& 18.46\%\end{array}$