Question

Paula is considering the purchase of a new car. She has narrowed her search to two cars that are equally appealing to her. Car A costs $22,000, and Car B costs $22,200. The manufacturer of Car A is offering 0% financing for 48 months with zero down, while the manufacturer of Car B is offering a rebate of $2000 at the time of purchase plus financing at the rate of 3%/year compounded monthly over 48 months with zero down. If Paula has decided to buy the car with the lower net cost to her, which car should she purchase

Answer 1

Car A has a net cost of $22,000 with 0% financing, while Car B has a net cost of $20,200 with a rebate of $2000 and financing at 3%/year compounded monthly over 48 months. Comparing the two options, Car B has the lower net cost and Paula should purchase it.

Step-by-step explanation:

To determine which car Paula should purchase, we need to calculate the net cost of each option.

For Car A, Paula would pay $22,000 with 0% financing, which means there are no additional costs or interest charges.

For Car B, Paula would pay $22,200 with a rebate of $2000, resulting in a net cost of $20,200. Additionally, she would have to pay interest on the remaining amount of $20,200 over 48 months with a rate of 3%/year compounded monthly.

To calculate the monthly payment for Car B, we can use the formula:

Monthly Payment = P * (r * (1+r)^n) / ((1+r)^n - 1)

Where P is the principal amount, r is the monthly interest rate, and n is the number of months.

Plugging in the values, we get:

Monthly Payment = $20,200 * (0.03/12 * (1+0.03/12)^48) / ((1+0.03/12)^48 - 1)

Calculating this gives us a monthly payment of approximately $451.16 for Car B.

Comparing the two options, Car A has a net cost of $22,000 and Car B has a net cost of $20,200. Therefore, Paula should purchase Car B as it has the lower net cost.