You are deciding whether to buy new or a two-year-old car (of othe same make) ba

Question

You are deciding whether to buy new or a two-year-old car (of  othe same make) based on which will cost you less when you reselll it at the end of three years. Your cost consist of two parts: the loss in the value of the car and the repairs. A new car costs $20,000 and loses 12% of its calue each year. Repairs are $400 the first year and increase by 18% each sunsequent year.

A) For a new car, find the first three terms of the sequence dN giving the depreciation (loss of value) in dollars in year n. Give a formula for dn.

C) Find the total cost of owning a new car for three years.

D) Find the total cost of ownung the two-year-old car for three years. Which should you by?

Explanation / Answer

A)NEW CAR:

d_n = 20000(0.12)(0.88)^(n-1)

D1=2400

D2=2112

D3=1858.56

dep first yr=0.12*20000

after first year value=0.88*20000

dep second yr=0.12*0.88*20000

after second year value=0.88*0.88*20000

dep third yr=0.12*0.88*0.88*20000

after third year value=0.88*0.88*0.88*20000

c)fixed cost=20,000

r_n = 400(1.18)^(n-1)

first yr repair=400

second yr repair=400*1.18=472

third yr repair=400*1.18^2=556.96

total cost=21428.96

d)cost of two yr old car=20000*0.88*0.88=15488

r_n = 400(1.18)^(n-1)

repair third yr=400*1.18^2=556.96

repair fourth yr=400*1.18^3=657.21

repair fifth yr=400*1.18^4=775.51

total cost=17477.68

since cost two yr old car is less,so we should buy it.

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