Question

Buying a Car

You are purchasing a new car for $27,600. The dealership offers you three options:
0% financing: 0 down and 0% financing for 48 months.
Rebate: 0 down. If you choose the rebate, you will need to secure a loan for the balance at your local bank.
Down payment: Make a down payment of 5% or more and get financing at 1.5% compounded monthly for 48 months.
Use this information to answer questions 3-6 below.
1. Use the Buying a Car information above to answer this question.
What is your monthly payment if you choose 0% financing for 48 months?
$ . Round to the nearest dollar.
2. The rebate offer is $2600, and you can obtain a car loan at your local bank for the balance at 5.02% compounded monthly for 48 months. If you choose the rebate, what is your monthly payment?
$ . Round to the nearest dollar.
3. You want to make monthly payments of $439, but you don't want a car loan over your head for more than 48 months, so you decide to go with the down payment option. How much of a down payment do you need to make?
$ . Round to the nearest dollar.
4. Suppose you make a down payment of 17% of $27,600 and finance the rest at 1.5% compounded monthly for 48 months. How much interest do you pay over the life of the loan?
$ . Round to the nearest dollar.

Answer 1

The monthly payment for 0% financing for 48 months is $575. If you choose the rebate, the monthly payment would be approximately $578. If you want to make monthly payments of $439 with 1.5% financing for 48 months, you would need to make a down payment of $0 or more. The interest paid over the life of the loan with a 17% down payment and 1.5% financing for 48 months would be $2,091.04.

Step-by-step explanation:

To calculate the monthly payment for 0% financing for 48 months, you can divide the total price of the car by the number of months: $27,600 / 48 = $575. This means your monthly payment would be $575.

If you choose the rebate option, you will need to secure a loan for the remaining balance. Using the given interest rate of 5.02% compounded monthly, you can use a loan calculator to determine the monthly payment. With a $2,600 rebate applied to the loan amount, the remaining balance would be $27,600 - $2,600 = $25,000. Plugging this amount into the loan calculator, the monthly payment would be approximately $578.

If you want to make monthly payments of $439 with 1.5% financing for 48 months, you can use a loan calculator to determine the amount of down payment needed. With 1.5% financing, you can find the loan amount by dividing the monthly payment by the monthly interest rate: $439 / 0.015 = $29,266.67. Subtracting the loan amount from the total price of the car gives you the down payment needed: $27,600 - $29,266.67 = -$1,666.67. Since a down payment cannot be negative, you would need to make a down payment of $0 or more.

To calculate the interest paid over the life of the loan with a 17% down payment and 1.5% financing for 48 months, you can find the loan amount by multiplying the total price of the car by (1 - down payment percentage): $27,600 * (1 - 0.17) = $22,932. With compounding monthly at 1.5%, you can use a loan calculator to find the total amount paid: $23,932 * (1 + 0.015)^48 = $25,023.04. Subtracting the loan amount from the total amount paid gives you the interest paid: $25,023.04 - $22,932 = $2,091.04.