Final answer:
To determine how expensive of a car Marie can afford, we use the present value of an annuity formula, considering her $250 monthly payment, 5-year loan term, and 7% annual interest rate. After calculating the loan amount, we can then calculate the total amount she will pay, including the interest over the life of the loan.
Step-by-step explanation:
To calculate the cost of the car that Marie can afford with a monthly payment of $250 at a 7% annual interest rate over 5 years, we can use the present value of an annuity formula:
PV = Pmt x ((1 - (1 + r)^-n) / r)
By calculating the loan amount, we find the maximum price of the car Marie can afford. The total money paid to the loan company is the monthly payment multiplied by the total number of payments. The total interest paid is this amount minus the original loan amount.
For the 5 year loan at 7% interest, we will plug in the values:
PV = $250 x ((1 - (1 + 0.0058333)^-60) / 0.0058333)
Once we have calculated PV, we can find the total amount paid by multiplying $250 by 60 (number of months) and then determine how much is paid as interest by subtracting the PV from the total amount paid.