Question

You want to buy a car, and a local bank will lend you $35,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 15%, with interest paid monthly. What is the monthly loan payment? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Here, the payments will be same every month, so it is an annuity. We will use the present value of annuity formula to calculate the monthly payments as per below:

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

where, PVA = Present value of annuity = $35000, P is the periodical amount, r is the rate of interest = 15%, so monthly rate = 15% / 12 = 1.25% and n is the time period = 60 months

Now, putting these values in the above formula, we get,

$35000 = P * (1 - (1 + 1.25%)^-60 / 1.25%)

$35000 = P * (1 - ( 1+ 0.0125)^-60 / 0.0125)

$35000 = P * (1 - ( 1.0125)^-60 / 0.0125)

$35000 = P * (1 - 0.47456760256) / 0.0125)

$35000 = P * (0.52543239743 / 0.0125)

$35000 = P * 42.0345917945

P = $35000 / 42.0345917945

P = $832.65

So, monthly loan payment is $832.65