Question

Jason bought a car for $40,000 upon graduation from college with an engineering degree and a very good job offer. A down payment of $5,000 was paid by his dad as a graduation gift. The rest of the amount was financed with Generous Motors at 6% nominal interest with 60 monthly payments, the first payment which is to start at the end of 13th month. Determine his monthly payment.

Answer 1

Answer:

Explanation:

The cost of the car = $40,000

Down payment = $5,000

Therefore loan amount on the car = Cost of the car - Down payment

= $40,000 - $5,000

= $35,000

But loan repayment starts from 13th months; therefore there are 12 months or 1 year for which interest amount will be added with the total loan amount

Total loan amount after one year = $35,000 * (1+6%) ^1 = $37,100

Now we can use PV of an Annuity formula to calculate the monthly payment of car loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV = $37,100

PMT = Monthly payment =?

n = N = number of payments = 60 months

i = I/Y = interest rate per year = 6%, therefore monthly interest rate is 6%/12 = 0.5% per month

Therefore,

$37,100 = PMT* [1- (1+0.005)^-60]/0.005

PMT = $37,100/51.72

= $717.38

Therefore correct answer is option A. $717.38