Question 8 of 15 , Step 1 of 1 $7 / 15$ JACQUELINE WALDRUM Will bought a new car and financed $\$ 14,000$ to make the purchase. He financed the car for 36 months with an APR of $3.5 \%$. Assuming he made monthly payments, determine the total interest Will paid over the life of the loan. Round your answer to the nearest cent, if necessary. Formulas Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts Submit Answer

Step 1 ：Given that Will financed a car for $14,000 at an APR of 3.5% for 36 months, we are to find the total interest he paid over the life of the loan.

Step 2 ：First, we need to convert the annual interest rate to a monthly interest rate. This is done by dividing the annual rate by 12. So, \(r = \frac{0.035}{12} = 0.002916666666666667\).

Step 3 ：Next, we calculate the monthly payment using the formula: \(P = \frac{r*PV}{1 - (1 + r)^{-n}}\), where P is the monthly payment, r is the monthly interest rate, PV is the present value or the amount of the loan, and n is the number of payments. Substituting the given values, we get \(P = \frac{0.002916666666666667*14000}{1 - (1 + 0.002916666666666667)^{-36}} = 410.2291161767497\).

Step 4 ：We then calculate the total amount paid over the life of the loan by multiplying the monthly payment by the number of payments: \(total\_paid = P*n = 410.2291161767497*36 = 14768.24818236299\).

Step 5 ：Finally, we calculate the total interest paid by subtracting the original loan amount from the total amount paid: \(total\_interest = total\_paid - PV = 14768.24818236299 - 14000 = 768.2481823629896\).

Step 6 ：Rounding to the nearest cent, the total interest Will paid over the life of the loan is approximately \(\boxed{768.25}\).