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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

Respuesta :

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

Answer:

d.) $18,350.00

Step-by-step 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 = [tex]\frac{0.096}{12}[/tex]   ( ∵ 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,

[tex]P=\frac{PV(r)}{1-(1+r)^{-n}}[/tex]

[tex]=\frac{13230(\frac{0.096}{12})}{1-(1+\frac{0.096}{12})^{-60}}[/tex]

≈ $ 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.

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