Question

Amy bought a new car for $38,000. She paid a 20% down payment and financed the remaining balance for 48 months with an APR of 4.5%. Determine the monthly payment that Amy pays. Round your answer to the nearest cent, if necessary.

a) $775.92

b) $789.47

c) $794.02

d) $802.36

Answer 1

Amy's monthly payment on a $38,000 car purchase with a 20% down payment and a financed balance at 4.5% APR for 48 months is closest to option (b) $789.47, calculated using the installment loan payment formula.

Step-by-step explanation:

Amy bought a new car for $38,000 and paid a 20% down payment. The remaining balance is financed for 48 months with an APR of 4.5%. To calculate the monthly payment, we first determine the down payment amount and the financed amount. A 20% down payment on $38,000 is $7,600 (20/100 × $38,000), leaving a balance of $30,400 to finance ($38,000 - $7,600).

To find the monthly payment, we can use the formula for an installment loan:

M = P × rac{r(1+r)^n}{(1+r)^n - 1}

where:

• M is the monthly payment
• P is the loan principal ($30,400)
• r is the monthly interest rate (APR divided by 12)
• n is the number of payments (48)

The monthly interest rate is 0.045 / 12 = 0.00375. Plugging these values into the formula gives us the monthly payment which can be calculated using a calculator or a spreadsheet tool.

The closest answer to the calculated monthly payment is option (b) $789.47, which suggests that is the monthly payment Amy needs to pay.