Suppose that you decide to buy a car for $$56,000,$ including taxes and license fees. You saved $$13,000$ for a down payment. The dealer is offering you a choice between two incentives. Incentive $A$ is $$3000$ off the price of the car, followed by a four$-$year loan at $6\mathrm{.}25\%.$

Incentive $B$ does not have a cash rebate, but provides free financing $($no interest$)$ over four years.

What is the difference in monthly payments between the two offers? Which incentive is the better deal? Use PMT $=\frac{P(\frac{r}{n})}{[1-(1+\frac{r}{n}{)}^{-nt}]}.$