91Ó°ÊÓ

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.

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

The compensating balance is $42,280.

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

The compensating balance is $21,140.

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

The effective interest rate is 25.8%.

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

The effective interest rate is 21.46%.

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

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.