Asset Depreciation - Logarithms How many years would it take for the value of a car purchased at 30

Trevor Wood

Trevor Wood

Answered question

2022-05-28

Asset Depreciation - Logarithms
How many years would it take for the value of a car purchased at 30 000 to fall to 15 000 if it depreciates by 15% in the first year and 12% every year after that? This is not actually graded homework, but I solved it iteratively (compounding down to 26000 at 15% and so on) and would like to solve it using logarithms to find n as well. The answer is 5 years based on the iterative method at which point it is 14800 or so.

Answer & Explanation

odczepneyv

odczepneyv

Beginner2022-05-29Added 10 answers

Let us call A the initial price, B the price after n years, a the depreciation rate for the first year and b the depreciation rate for the following years. When you built your formula, I suppose that you noticed the following relation
B = A ( 1 a ) ( 1 b ) n 1
So, going to logarithms is a very good way for finding n. For your example A = 30 , 000, B = 15 , 000, a = 0.15, b = 0.12 lead to n = 5.15094.
It seems that, probably because of some rounding, we do not get exactly the same result

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