Question

Valley auto sold a used car priced at $10 600 for 10% down and the balance to be paid in equal monthly payments over four years at 7 .2% compounded monthly. how much does the buyer have to pay at the end of each month?

Answer 1

After accounting for a 10% down payment and a 7.2% monthly interest rate over 4 years, the buyer at Valley Auto needs to make monthly payments of approximately $229.33 to settle the car loan.

Calculating the Monthly Payment for the Used Car

Here's how to determine the monthly payment for the used car purchased from Valley Auto:

1. Calculate the loan amount:

Down payment = 10% of $10,600 = $1,060

Loan amount = Car price - Down payment = $10,600 - $1,060 = $9,540

2. Apply the monthly interest rate:

Annual interest rate = 7.2%

Monthly interest rate = 7.2% / 12 = 0.6%

3. Use the loan formula to calculate the monthly payment:

M = P * (r(1+r)^n) / ((1+r)^n - 1)

M = Monthly payment

P = Loan amount = $9,540

r = Monthly interest rate = 0.006

n = Total number of payments = 4 years * 12 months/year = 48

4. Calculate the monthly payment:

M = $9,540 * (0.006 * (1 + 0.006)^48) / ((1 + 0.006)^48 - 1)

M = $229.33 (approximately)

Therefore, the buyer needs to pay $229.33 at the end of each month for four years to settle the car loan.

Note: This calculation assumes that the loan has no additional fees or charges. It's essential to carefully review the loan agreement for any additional costs associated with the financing.