# 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)?

mathsworkmusic | (Level 2) Educator

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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

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