Katy buys a car for 20500 In 3 years the value of the car is

Katy buys a car for $20,500. In 3 years the value of the car is $14,500. Suppose that 6 years after Katy purchased her car, the manufacturer stops producing the model that she purchased. this manufacturing decision causes the value of the car to begin to appreciate. After 8 years of ownership, Katy\'s car is now worth $900 more than it was worth after 6 years. The depreciation and appreciation of the car\'s value model linear functions. What is the value of Katy\'s car after 10 years?

Solution

Let the annual depreciation in Katy\'s car for the 6 years from purchase, i.e. till the manufacturer stopped manufacturing this moded, be $ x and let the annual appreciation thereafter be $ y. Since the depreciation and appreciation of the car\'s value model linear functions, therefore, 14500 = 20500 - 3x or, 3x = 20500- 14500 = 6000 so that x = 6000/3 = 2000. Then 6x = 6*2000= 12000, so that the worth of Katy\'s car after 6 years of ownership is 20500 - 6x = 20500 - 12000 = $ 8500. After 8 years of ownership, Katy\'s car is now worth $900 more than it was worth after 6 years, i.e its worth is now 8500 + 900 = $ 9400. Thus, in 2 years, the worth of Katy\'s car has incresed by $ 900 so that the annual appreciation in the worth of Katy\'s car after 6 years of ownership is $ 900/2., i.e. $ 450 per annum.Thus, the value of Katy\'s car after 10 years is $ 9400 + 2*450 = 9400 + 900 = $10300. The answer c is correct.