John bought a 2-year-old car for £ 12 000. Three years later he decides to sell the car; "I think that the value of the car is inversely proportional to its age". John estimates the value of the car using this idea. The actual value of the car depreciates by 20% each year. Work out the difference between John's estimate and the actual value.

Question

Mathematics

Ruby Hooper

24 May, 22:52

John bought a 2-year-old car for £ 12 000. Three years later he decides to sell the car; "I think that the value of the car is inversely proportional to its age". John estimates the value of the car using this idea. The actual value of the car depreciates by 20% each year. Work out the difference between John's estimate and the actual value.

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Answers (1)

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Pippin · Answer 1

Actual value after 5 years is £1344 more than John's value.

Step-by-step explanation:

Johns estimate:-

V = k/t (inverse proportionality) where V = value of the car and t = it's age.

When t = 2, V = £12,000:-

12,000 = k/2 giving k = 24,000

Therefore the value at 5 years of age, according to John's proposition is

V = 24,000 / 5 = £4,800

The actual value using the given depreciation is

12000 (1 - 0.2) ^3 = £6144

Difference is £1344