You purchase an automobile for $20, 000. After some research, you learn that you

Question

You purchase an automobile for $20, 000. After some research, you learn that you can expect the costs and salvage values shown in the table below. The maintenance, insurance, and operating costs are listed in dollars for the particular year; the TOTAL row is the sum of the maintenance, insurance, and operating costs for the appropriate year. The salvage value is the worth of the automobile at the end of the listed year; i.e. the car is worth $14, 400 if sold at the end of year 1, $9, 300 if sold at the end of year 2, and so on. The bottom row in the table show s the annualized cost of owning and operating the car for the number of years appropriate to the column. The calculations involve an interest rate of 6%. For example, the annual cost of owning and operating this automobile if you buy it, operate it for two years, and then sell it is $12, 608.98 per year, the result of the following calculation: [-20, 000 - 6, 500(P/F, 6%, 1) - 4, 800(P/F, 6%, 2) + 9, 300(P/F, 6%, 2)](A/P, 6%, 2) [-20, 000 - 6, 500(0.9434) - 4, 800(0.8900) + 9, 300(0.8900)](0.54544) [-20, 000 - 6, 132.10 - 4, 272 + 8, 277](.54544) -22, 127.10(.54544) = -12, 069.01 Find the annual cost of owning and operating this automobile if you keep it for three years. Round your answer to the nearer dollar._____

Explanation / Answer

For 3 Years

= [-20000-6500(P/F,6%,1)-4800(P/F,6%,2)-4500(P/F,6%,3)+4200(P/F,6%,3)](A/P,6%,3)

= [-20000-6500(0.9434)-4800(0.8900)-4500(0.8396)+4200(0.8396)](0.37411)       

= $11,468

For 5 Years

= [-20000-6500(P/F,6%,1)-4800(P/F,6%,2)-4500(P/F,6%,3)-5400(P/F,6%,4)-7800(P/F,6%,5)+ 3000(P/F,6%,5)](A/P,6%,5)

= [-20000-6500(0.9434)-4800(0.8900)-4500(0.8396)-5400(0.7921)-7800(0.7473)+ 3000(0.7473)](0.2374)

= $9,982

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