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A car is bought for $45, 200. The insurance company decided to calculate the depreciation each year as 14.5% of the book value at the beginning of the year. Determine the value of the car at the end of 6 years.

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Using the exponential Decay relation, the value of the car after 6 years will be :$17657.740

Using the exponential decline relation :

  • A(1 - r)^t

  • A = initial value ; r = Rate ; t = time

Final value of car after 6 years :

Final value = 45200(1 - 0.145)^6

Final value = 45200(0.855)^6

Final value = 45200(0.390657969445640625)

Final value = 17657.740

Therefore, the final value of the car after six years is $17657.740

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