Question 8 of 15 , Step 1 of 1
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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.
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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 \(\boxed{768.25}\).