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