Question

Suppose that you decide to buy a car for $61,000, 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 $5000 off the price of the car, followed by a five-year loan at 7.24%. Incentive B does not have a cash rebate, but provides free financing (no interest) over five years. Р What is the difference in monthly payments between the two offers? Which incentive is the better deal?

Answer 1

To find the difference in monthly payments between the two car incentives, calculate the monthly payment for each. Subtract the monthly payment of Incentive B from the monthly payment of Incentive A to determine the difference. The incentive with the lower monthly payment is the better deal.

Step-by-step explanation:

To find the difference in monthly payments between the two offers, we need to calculate the monthly payment for each incentive. Let's start with Incentive A.

For Incentive A, the price of the car after the $5000 discount is $61,000 - $5000 = $56,000. To calculate the monthly payment, we use the formula for a loan:

Monthly Payment = Principal * (1 + Interest Rate / Number of Payments) / Number of Payments

Substituting the values, we get:

Monthly Payment for Incentive A = $56,000 * (1 + 0.0724 / 12) / (12 * 5)

Next, let's calculate the monthly payment for Incentive B. Since there is no interest, the principal remains $61,000. Using the same formula:

Monthly Payment for Incentive B = $61,000 / (12 * 5)

To find the difference in monthly payments, subtract the monthly payment for Incentive B from the monthly payment for Incentive A:

Difference in Monthly Payments = Monthly Payment for Incentive A - Monthly Payment for Incentive B

The incentive with the lower monthly payment would be the better deal.