Question 7 of 15 , Step 1 of 1
$5 / 15$
2
Jenna bought a new car for $\$ 32,000$. She paid a $20 \%$ down payment and financed the remaining balance for 72 months with an APR of $6.5 \%$. Determine the monthly payment that Jenna pays. Round your answer to the nearest cent, if necessary.

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Step 1 ：First, calculate the down payment by finding 20% of the total cost of the car. This can be done by multiplying the total cost of the car, $32,000, by 20%. This gives us a down payment of $6,400.

Step 2 ：Next, subtract the down payment from the total cost of the car to find the amount that Jenna financed. This can be done by subtracting $6,400 from $32,000, which gives us $25,600.

Step 3 ：Then, calculate the monthly interest rate by dividing the annual interest rate, 6.5%, by 12. This gives us a monthly interest rate of approximately 0.005416666666666667.

Step 4 ：Now, use the formula for calculating the monthly payment for a loan, which is \(M = P[r(1 + r)^n] / [(1 + r)^n – 1]\), where M is the monthly payment, P is the principal loan amount, r is the monthly interest rate, and n is the number of payments. Plugging in the values we have, we get a monthly payment of approximately $430.33.

Step 5 ：Finally, round the monthly payment to the nearest cent to get the final answer. Jenna's monthly payment is \(\boxed{430.33}\).