Question

Valerie is going to purchase a new car. the car she wants has a list price of $32,495. valerie is planning to make a down payment of $1,877. furthermore, she plans to trade in her current car, which is a 2006 hyundai sonata in good condition. she will finance the rest of the cost by making monthly payments over five years. she can finance the cost at a rate of 8.64%, compounded monthly. she will also have to pay 8.23% sales tax, a $2,243 vehicle registration fee, and a $314 documentation fee. if the dealer gives valerie 87.5% of the trade-in price on her car, listed below, approximately how much will valerie pay in total for her new car? (round all dollar values to the nearest cent, and consider the trade-in to be a reduction in the amount paid.) hyundai cars in good condition model/year 2004 2005 2006 2007 sonata $6,145 $6,520 $6,784 $7,066 tiburon $6,880 $7,144 $7,382 $7,785 elantra $4,211 $4,425 $4,598 $4,880 accent $5,676 $5,828 $6,005 $6,317 a. $37,385 b. $38,821 c. $38,287 d. $36,944

Answer 1

Valerie will pay approximately $49,820.08 in total for her new car.

Step-by-step explanation:

To calculate the total cost that Valerie will pay for her new car, we need to consider the list price of the car, her down payment, trade-in value, taxes, and fees.

1. List price of the car: $32,495

2. Down payment: $1,877

3. Trade-in value: Valerie's current car is a 2006 Hyundai Sonata, and the dealer gives 87.5% of the trade-in price. The trade-in price of the 2006 Hyundai Sonata is $6,784, and 87.5% of $6,784 is $5,951.

4. Remaining cost after down payment and trade-in value: $32,495 - $1,877 - $5,951 = $24,667

5. Taxes and fees: Valerie needs to pay 8.23% sales tax, which is 8.23% of $24,667 = $2,030.19. She also needs to pay a $2,243 vehicle registration fee and a $314 documentation fee. The total amount for taxes and fees is $2,030.19 + $2,243 + $314 = $4,587.19.

6. Financing the rest: Valerie will finance the remaining cost over five years at an interest rate of 8.64% compounded monthly. We can use the formula for the future value of an ordinary annuity to calculate the total amount that Valerie will pay in monthly payments. FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the total number of payments. Plugging in the values, the total amount Valerie will pay for financing is $24,667 * ((1 + 0.0864/12)^(5*12) - 1) / (0.0864/12) = $25,153.08.

7. Total cost: To calculate the total cost, we need to add the remaining cost after down payment and trade-in value and the amount paid for financing. Total cost = $24,667 + $25,153.08 = $49,820.08.

Therefore, Valerie will pay approximately $49,820.08 in total for her new car.