Question

Tim Smith is shopping for a used luxury car. He has found one priced at $ 27000.

The dealer has told Tim that if he can come up with a down payment of ​$5 600​, the dealer will finance the balance of the price at a 7​% annual rate over 3 years ​(36 ​months).

​(Hint: Use four decimal places for the monthly interest rate in all your​ calculations.)

a.  Assuming that Tim accepts the​ dealer's offer, what will his monthly​ (end-of-month) payment amount​ be?

b.  Use a financial calculator or spreadsheet to help you figure out what​ Tim's monthly payment would be if the dealer were willing to finance the balance of the car price at an annual rate of 3.9​%?

Thanks!

Answer 1

1. Assuming that Tim accepts the​ dealer's offer, what will his monthly​ (end-of-month) payment amount​ be?

Price of Car = $27,000

Down payment = $5,600

Loan amount = car price – down payment = $27,000 - $5,600 = $21,400

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 of loan = $21,400

PMT = Monthly payment =?

n = N = number of payments = 36 months

i = I/Y = interest rate per year = 7%, therefore monthly interest rate is 7%/12 = 0.5833% per month

Therefore,

$21,400 = PMT* [1- (1+0.5833%) ^-36]/0.5833%

= $660.77

Monthly payment of car loan is $660.77

2. Use a financial calculator or spreadsheet to help you figure out what​ Tim's monthly payment would be if the dealer were willing to finance the balance of the car price at an annual rate of 3.9​%?

We can use PV of an Annuity formula to calculate the monthly payment of car loan at 3.9% annual interest rate

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

Where PV of loan = $21,400

PMT = Monthly payment =?

n = N = number of payments = 36 months

i = I/Y = interest rate per year = 3.9%, therefore monthly interest rate is 3.9%/12 = 0.325% per month

Therefore,

$21,400 = PMT* [1- (1+0.325%) ^-36]/0.325%

= $630.86

Monthly payment of car loan is $630.86