SOLUTION: Hugh Feridan bought a new car for $18,200. He estimates the car will be worth $11,600 in 3 years. What is the estimated average annual depreciation? What is the estimated rate of d

Question 1178904: Hugh Feridan bought a new car for $18,200. He estimates the car will be worth $11,600 in 3 years. What is the estimated average annual depreciation? What is the estimated rate of depreciation to the nearest whole percent?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the original value of the car is 18200.
the value of the car in 3 years is 11600.

the average annual depreciation for the 3 years is (18200 - 11600) / 3 = 2200 per year.

the average annual rate of depreciation for the 3 years is 11600 / 18200 ^ (1/3) - 1 = -.1384115982 * 100 rounded to the nearest whole number = -14%.

you can graph these two and you will see that one will give you straight line depreciation, where the same amount of value is deducted each year, and the other will give you exponential rate of depreciation where the same rate of value is deducted each year.

the close up graph looks like this:

the far out graph looks like this:

what these graphs tell you is:

at the 3 year mark, the value of the car is the same, as expected.

with the same amount of depreciation each year graph, the car fully depreciates in little more than 8 years.

with the same rate of depreciation each year graph, the car doesn't ever fully depreciate.

this is why, in real life, same rate of depreciation per year switches to straight line depreciation as the car ages past a certain number of years.

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