Question

Susan is considering buying a 2017 Smart ForTwo costing $21,635 and finds that the retaining values of the vehicle over the next five years are as follows: • Percent of the total value retained after 36 months: 28% • Percent of the total value retained after 60 months: 17% If her interest rate is 6% compounded annually, what is the ownership cost of the vehicle over three years? five years? Click the icon to view the interest factors for discrete compounding when i = 6% per year. The ownership cost of the vehicle over three years is $ (Round to the nearest dollar.) The ownership cost of the vehicle over five years is $ (Round to the nearest dollar.)

Answer 1

Price = $ 21,635

Percent of value retained after 36 months = 28%

Salvage value = 0.28×21635 = $ 6,057.8

Percent of value retained after 60 months = 17%

Salvage value = 0.17 × 21,635 = $ 3,677.95

Interest rate = 6%

Capital cost of the car for 3 years

CR= (I - S) (A/P,i%,n) + iS

CR = (21,635 - 6,057.8) (A/P.6%.3) +0.06 x 6,057.8

$\large CR = 15,577.20\times 0.3741 + 363.45$

$\large CR = \$ \ 6,191.05$

$\large CR \approx \$ \ 6,191$

Now calculating for 5 years

$\large CR = (21,635 -3677.95 ) (A/P,6\%,5) +0.06\times 3677.95$

$\large \implies CR = 17,957.05\times \frac{0.06}{1-1.06^{-5}} + 220.677$

$\large \implies CR = 17,957.05\times 0.237396 + 220.677$

$\large \implies CR = \$ \ 4,483.62$

$\large \implies CR \approx \$ \ 4,484$