Question

You have purchased a used car today at a price of nineteen thousand dollars. You made a down payment of $2,800 and financed the rest by making monthly payments of $272 starting a month from today. Which of the following best describes the terms of your loan?
a. 6.5% APR for 7 years

b. 6.5% APR for 3 years

c. 6.5% APR for 4 years

d. 6.5% APR for 5 years

e. 6.5% APR for 6 years

Answer 1

It is clear from the options that APR is 6.5%. So use the equation of present value of annuity to find n

Present value of Annuity = A*[(1-(1+r)^-n)/r]

Where

A - Annuity payment = 272

r - rate per period = 6.5%/12 = 0.00541666666

n - no. of periods = ?

19000-2800 = 272*[(1-(1+0.00541666666)^-n)/0.00541666666]

(1-(1+0.00541666666)^-n)= 16200*0.00541666666/272

= 0.32261029372

1.00541666666^-n = 1-0.32261029372

= 0.67738970628

-n = log 0.67738970628/ log 1.00541666666

= -0.16916140724/0.00234608019

n = 72.1038470727 months

= 72.1038470727/12 years

n = 6 years