Final answer:
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.