Question

Amy bought a new car for $39,000 . she paid a 10% down payment and financed the remaining balance for 60 months with an apr of 5.5% . determine the monthly payment that amy pays. round your answer to the nearest cent, if necessary.

Answer 1

To determine Amy's monthly car payment, the down payment is subtracted from the purchase price and the remaining balance is amortized over 60 months at an APR of 5.5%. Amy's monthly payment is calculated using the formula for an installment loan.

Step-by-step explanation:

The question involves calculating the monthly car payment Amy would have to make on her new car purchase after a down payment and financing the remaining balance at a given APR for a set period. The steps in solving this finance problem are as follows:

1. Calculate the down payment by taking 10% of the $39,000 car price, which is $3,900.
2. Subtract the down payment from the car price to find the amount financed: $39,000 - $3,900 = $35,100.
3. Use the loan formula or an online loan calculator to determine the monthly payment based on the balance of $35,100, an APR of 5.5% convertible monthly, and a term of 60 months.

To find the monthly payment manually, the loan formula is used: M = P[r(1+r)^n]/[(1+r)^n-1], where M is the monthly payment, P is the principal balance ($35,100), r is the monthly interest rate (APR/12), and n is the number of payments (60).

Car loans are a significant financial commitment and understanding the terms of the loan, including the APR and the length of the loan, are key considerations when purchasing a vehicle. For Amy, she needs to consider if she's comfortable with the monthly payment based on a 5-year (60 months) loan duration.