# Corrine bought a car for $15,000 and its value depreciated linearly. After 3 years, the value of the car was $11,250. If instead the car depreciated by a fixed percentage each year, what amount...

Corrine bought a car for $15,000 and its value depreciated linearly. After 3 years, the value of the car was $11,250. If instead the car depreciated by a fixed percentage each year, what amount of depreciation would be subject to AMT (Alternative Minimum Tax)?

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The AMT (alternative minimum tax) is applicable to depreciation above that of the straight line method.

If the value of the car depreciates linearly (in a straight line) then the amount of depreciation per year is fixed at (15000-11250)/3 = $1,250.

Supposing that instead we assumed that the car depreciates by a fixed *percentage* each year (compound depreciation) so that the depreciation is accelerated at the beginning of the three-year period compared to linear depreciation.

Given that the final value of the car is $11,250 the annual percentage rate (APR) of depreciation is

`d = (11250/15000)^(1/3) = 0.909 `

ie the car depreciates by roughly 10% in value each year. The absolute depreciation in the ith year under this model is given by

`15000a^(i-1) - 15000a^i`

Compare the depreciations each year from the two models:

Percentage: 1371.60 1246.18 1132.23

Straight line: 1250.00 1250.00 1250.00

Difference: 121.60 -3.82 -117.77

Using the percentage depreciation model, only the depreciation in the first year is greater than that when using the straight line method.

**So the total amount subject to AMT over the three years is $121.60**