Asked by College Student
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.
Answers
Answered by
GPT 3.5
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.
$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.