Suppose that you decide to buy a car for ​$58 comma 000

Question

​,
including taxes and license fees. You saved $ 11 comma 000

for a down payment. The dealer is offering you a choice between two incentives.
Incentive A is ​$6000

off the price of the​ car, followed by a four
​-year
loan at 7.08
​%.
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 equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction
.

Answer 1

For incentive A, the loan amount would be $58,000 - $6,000 (rebate) - $11,000 (down payment) = $41,000. Using the loan payment formula P[r/n]/[1-(1+r/n)^(-nt)], where P is the loan amount, r is the annual interest rate in decimal form (0.0708), n is the number of payments per year (12), and t is the number of years (4), the monthly payment would be calculated as $41,000[0.0708/12]/[1-(1+0.0708/12)^(-12*4)] = $1,000.32.

For incentive B, the loan amount would simply be $58,000 - $11,000 (down payment) = $47,000, and because there's no interest, the monthly payment would simply be $47,000 / (4 * 12) = $979.17.

So the difference in monthly payments between the two offers would be $1,000.32 - $979.17 = $21.15.

The incentive with the lower monthly payment is incentive B (the no-interest loan), so that would be the better deal.

In conclusion, the difference in monthly payments between the two offers is $21.15, and Incentive B is the better deal.