Michelle bought a new car for $37,000. She paid a 10% down payment and financed the remaining balance for 48 months with an APR of 4.5 % . Determine the monthly payment that Michelle pays. Round your answer to the nearest cent, if necessary.

Answer 1

To determine the remaining balance that Michelle financed, we first need to find 90% of the total cost of the car:

$37,000 * 0.90 = $33,300

The remaining balance that Michelle financed is $33,300.

Next, the monthly payment can be calculated using the formula for a fixed-rate amortizing loan:

PMT = P [(r(1+r)^n) / ((1+r)^n - 1)]

Where:
PMT = monthly payment
P = principal loan amount ($33,300)
r = monthly interest rate (APR / 12 = 4.5% / 12 = 0.375% = 0.00375)
n = total number of payments (48)

Now, plug in the values to find the monthly payment:

PMT = $33,300 * [0.00375*(1+0.00375)^48] / [(1+0.00375)^48 - 1]

PMT = $674.97

Therefore, Michelle pays a monthly payment of $674.97 to finance the remaining balance of her car loan.