Question

Frank purchased a car for $14,870. He made a down payment of $1,640. He applied for a five-year installment loan with an interest rate of 9.6%. What is the total cost of the car after five years?

a.) $14,500.08
b.) $16,297.52
c.) $16,710.00
d.) $18,350.00

Answer 1

i belive the answer is D but if i am wrong please let me lnow

Answer 2

d.) $18,350.00

Explanation:

Given,

The original value of the car = $ 14,870,

Down payment = $ 1,640,

So, the present value of the loan, PV = original value - down payment

= $ 14,870 - $ 1,640,

= $ 13,230,

Rate of interest per year = 9.6% = 0.096,

So, the monthly rate, r =
`(0.096)/(12)` ( ∵ 1 year = 12 months )

Time = 5 years,

So, the number of installments, n = 12 × 5 = 60,

Thus, the amount of each installment of the loan,

`P=(PV(r))/(1-(1+r)^(-n))`

`=(13230((0.096)/(12)))/(1-(1+(0.096)/(12))^(-60))`

≈ $ 278.50,

Hence, the total value of the car after 5 years = each installment × number of installments + down payment

= 278.50 × 60 + 1640

= 16710 + 1640

= $ 18,350.00

i.e. OPTION d) is correct.