Question

A car dealer offers to buy your car for $9,800 so that you can purchase a new one. If your monthly payment is $554.23 with an annual interest rate of 4.8% and you have 20 more payments remaining, is the present value of your car loan more or less than the amount the dealer is offering? By how much? (Round your answer to the nearest cent.)

Answer 1

The present value of your car loan is $9,173.17, which is less than the amount the dealer is offering by $626.83.

Step-by-step explanation:

To determine whether the present value of your car loan is more or less than the amount the dealer is offering, we need to calculate the present value of your remaining payments. We can use the formula for present value of an annuity:

Present Value = Payment Amount × (1 - (1 + Interest Rate)^-Number of Periods) / Interest Rate

Using the given values, we can calculate the present value of your loan:

Present Value = $554.23 × (1 - (1 + 0.048/12)^-20) / (0.048/12)

After calculating, we find that the present value of your car loan is $9,173.17. Since the dealer is offering $9,800 for your car, the present value of your car loan is less than the amount the dealer is offering by $626.83.