Question

Tom is considering purchasing a £21,500 car. After five years, he will be able to sell the vehicle for £7,500. Petrol costs will be £2,300 per year, insurance £700 per year, and parking £600 per year. Maintenance costs will be £950, rising by £400 per year thereafter.

The alternative is for Tom to take taxis everywhere. This will cost an estimated £7,500 per year. Tom will rent a vehicle each year at a total cost (to year-end) of £700 for the family vacation, if he has no car. If Tom values money at 10% annual interest, should he buy the car? Use an annual worth comparison method {Perform all calculations using 5 significant figures and round any monetary answers to the nearest cent}.

The annual cost of operating an Auto is: ?

The annual cost of using taxis as an alternative is: ?

Which option should Tom take?

Answer 1

Option 1 : Using a car(Note : All amounts are in pounds)

Year 1 Year 2 Year 3 Year 4 Year 5

Purchase cost 21500

Petrol cost 2300 2300 2300 2300 2300

Insurance cost 700 700 700 700 700

Parking fee 600 600 600 600 600

Maintenance cost 950 1350 1750 2150 2550

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Total cost before interest 26050 4950 5350 5750 6150

Annual interest cost (at 10%) 2605 495 535 575 615

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Total cost after interest   28655 5445 5885 6325 6765   

Money obtained from sale (-) 7500

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Total cost of option 1 = 28655 + 5445 + 5885 + 6325+6765 - 7500 = 45575

Option 2 : Taking a taxi

   Year 1 Year 2 Year 3 Year 4 Year 5

Taxi cost 7500 7500 7500 7500 7500

Family vacation cost 700 700 700 700 700

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Total cost before interest 8200 8200 8200 8200 8200

Interest cost (at 10%) 820 820 820 820 820

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Total cost after interest 9020 9020 9020 9020 9020

Total cost of option 2 = 9020 * 5 = 45100

Thus option 2 is better with less total cost (you save 45575-45100 = 475 pounds) .Annual cost for each option for each of the 5 years is shown above.