Question

Chris is shopping for a new car. He will put $2000 down, and finance the rest with 48 monthly payments at an interest rate of 8%. If he can afford monthly payments of $300 per month, what is the price of the most expensive car that he can afford?

Answer 1

To determine the price of the most expensive car Chris can afford, calculate the loan amount using the present value of annuity formula.

Step-by-step explanation:

To determine the price of the most expensive car that Chris can afford, we need to calculate the total loan amount. Chris will put $2000 down, which means he needs to finance the rest of the car price. Let's assume the car price is x dollars, so the loan amount will be x - $2000.

The loan amount can be calculated using the formula for the present value of an annuity:

Loan Amount = Monthly Payment * [(1 - (1 + interest rate)^(-number of months)) / interest rate]

Plugging in the given values, we have:

x - $2000 = $300 * [(1 - (1 + 0.08/12)^(-48)) / (0.08/12)]

Now, we can solve this equation to find the value of x, which will give us the maximum price of the car that Chris can afford.