Question

The value of a piece of industrial equipment

depreciates after it is purchased. Suppose that
the depreciation follows an exponential decay
model. The value of the equipment at the end
of 8 years is $30,000 and its value has been
decreasing at the rate of 7.5% per year.
Find the initial value of the equipment when it
was purchased.

Answer 1

$55,974.14

Explanation:

You want the initial value of a piece of equipment that has depreciated to $30,000 after 8 years at the rate of 7.5% per year.

Model

The exponential model of value is ...

A = P(1 - rate)^t

where A is the current value, P is the initial value, and r is the rate of depreciation per year for t years. Solving for P, we have ...

P = A/(1 -rate)^t = P·(1 -rate)^-t

P = 30000(1 -0.075)^-8 ≈ 55974.14

The initial value of the equipment was about $55,974.14.

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