Question

Colin bought a new car and financed $24,000 to make the purchase. He financed the car of 72 months with an APR of 6.5%. Assuming he made monthly payments, determine the total interest Colin paid over the life of the loan. Round your answer to the nearest cent, if necessary.

Answer 1

To calculate the total interest paid, use the formula for calculating the monthly payment on a loan and subtract the principal amount from the total amount paid. In this case, Colin paid a total of $5,685.60 in interest over the life of the loan.

Step-by-step explanation:

To calculate the total interest paid, we can use the formula for calculating the monthly payment on a loan:

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

Where P is the principal amount ($24,000), r is the monthly interest rate (6.5% / 12), and n is the total number of months (72).

Substituting the values into the formula and solving for the monthly payment, we get:

Monthly Payment = $402.90

Therefore, Colin would have made monthly payments of $402.90 over the life of the loan. To calculate the total interest paid, we can subtract the principal amount from the total amount paid:

Total Interest Paid = (Monthly Payment * n) - P

Substituting the values, we get:

Total Interest Paid = ($402.90 * 72) - $24,000

= $5,685.60

Colin paid a total of $5,685.60 in interest over the life of the loan.