Question

A car dealership is offering to roll over the amount owed on your car into a new loan so you can purchase a new car. Suppose you owe $5,606.77 on your current car and have agreed to a new car whose total cost, including tax and license, is $22,905.87. You are getting a 5-year loan at an annual interest rate of 3.75%. What are your new monthly payments (in dollars)? (Round your answer to the nearest cent.)

Answer 1

To find the new monthly payments after rolling over an existing car loan balance to a new loan, we calculate the total loan amount and apply the amortizing loan formula. The monthly payment comes out to $520.75 when rounded to the nearest cent.

Step-by-step explanation:

To calculate the new monthly payments for a car loan after rolling over the previous balance into a new loan, we will use the formula for an amortizing loan which includes the principal and the interest. The formula for the monthly payment M is:

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

Where:

• P is the principal amount
• i is the monthly interest rate
• n is the total number of payments (months)

In this case, we have:

• Total owed on current car: $5,606.77
• Cost of new car including tax and license: $22,905.87
• Total loan amount (principal P): $5,606.77 + $22,905.87 = $28,512.64
• Annual interest rate: 3.75%
• Monthly interest rate (i): 3.75% / 12 = 0.3125%
• Loan term: 5 years or 60 months (n)

The formula becomes:

M = 28512.64 * (0.003125 / (1 - (1 + 0.003125)^-60))

After calculating, we find that the new monthly payments, rounded to the nearest cent, are:

Monthly Payments = $520.75