The price of a new car is $16,000. Assume that an individual makes a down paymen
ID: 3122278 • Letter: T
Question
The price of a new car is $16,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 7%/year compounded monthly. (Round your answers to the nearest cent.) (a) What monthly payment will she be required to make if the car is financed over a period of 24 months? Over a period of 72 months? 24 months $ 72 months $ (b) What will the interest charges be if she elects the 24-month plan? The 72-month plan? 24-month plan $ 72-month plan $
Explanation / Answer
Given that:
The price of a new car is = $16,000
Down payment = 25 % of the price of new car
therefore loan amount = 16000 - 25%of 16000
= 16000 - 4000
= 12000
Rate of interest = r%/12 = 7%/12 ( compounded monthly)
r = 0.07/12
Payment = loan amount [ r/(1 -(1+r)-n ) ]
n = no of months for payment
for n = 24 months
Payment = 12000 [(0.07/12 )/( 1-(1+0.07/12)-24)]
= 12000 x 0.04477
= $ 537.27
$ 537.27 monthly payment will she be required to make if the car is financed over a period of 24 months
Now,
for n = 72 months
for n = 24 months
Payment = 12000 [(0.07/12 )/( 1-(1+0.07/12)-72)]
= 12000 x 0.01705
= $ 204.59
$ 204.59 monthly payment will she be required to make if the car is financed over a period of 72 months
(b)
the interest charges be if she elects the 24-month plan = total money paid monthly over 24 months - Loan amount
= $ 537.27 x 24 - 12000
= 894.48
the interest charges be if she elects the 72-month plan = total money paid monthly over 72 months - Loan amount
= $ 204.59 x 72 - 12000
= $ 2730.48
Answer :24-month plan $ 894.48 and 72-month plan $2730.48
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