Answer
The amount of difference in monthly payment is \[\$10\]and Incentive A is a better deal.
Work Step by Step
The amount of difference in monthly payments is to be computed by calculating the regular monthly payments under two incentives given, that is, Incentive A and Incentive B.
Calculate the amount of monthly payment while financing under Incentive A where a cash rebate of $10,000 is allowed and by following the terms of loan under that the costs of a car is $56,000 including taxes and license fees and a saving of $8,000 as a down payment for 4 years at 12.5%.
$\begin{align}
& PMT=\frac{P\left( \frac{r}{n} \right)}{\left[ 1-{{\left( 1+\frac{r}{n} \right)}^{-nt}} \right]} \\
& =\frac{\left( \$56,000-\$8,000-\$10,000\right)\left(\frac{0.125}{12}\right)}{\left[1-{{\left(1+\frac{0.125}{12}\right)}^{-12\left(4\right)}}\right]}\\&=\frac{\left(\$38,000\right)\times0.0104}{\left[1-{{\left(1+0.0104\right)}^{-48}}\right]}\\&=\frac{\$39.5833}{0.048669}\end{align}$
$=\$813$
Calculate the amount of monthly payment while financing under Incentive B under that the costs of a car is $56,000 including taxes and license fees and a saving of $8,000 as a down payment for 4 years at no interest.
$\begin{align}
& PMT=\frac{\left( \text{Purchase Price}-\text{Down Payment} \right)}{\left( n\times 12 \right)} \\
& =\frac{\left( 56,000-8,000 \right)}{\left( 4\times 12 \right)} \\
& =\$1,000\end{align}$
Calculate the amount of difference in monthly payments while financing a car under two incentives.
\[\begin{align}
& \text{Amount of difference}=\left( \begin{align}
& \text{Monthly payment under Incentive A} \\
& -\text{Monthly payment under Incentive B} \\
\end{align} \right) \\
& =\left( 813-1,000 \right) \\
& =\$187\end{align}\]
Hence, the amount of difference in monthly payment is \[\$10\]and Incentive A is a better deal.
