Question

A piece of manufacturing equipment valued at $125000 depreciates at a steady rate of 10% per year. What is the value of the equipment in 15 years?

Answer 1

The value of the equipment in 15 years will be $25,736

Explanation:

The value of the equipment after t years is given by the following equation:

`V(t) = V(0)(1-r)^(t)`

In which V(0) is the initial value and r is the yearly depreciation rate, as a decimal.

A piece of manufacturing equipment valued at $125000 depreciates at a steady rate of 10% per year.

This means that
`V(0) = 125000, r = 0.1`

Then

`V(t) = V(0)(1-r)^(t)`

`V(t) = 125000(1-0.1)^(t)`

`V(t) = 125000(0.9)^(t)`

What is the value of the equipment in 15 years?

This is V(15).

`V(15) = 125000(0.9)^(15) = 25736`

The value of the equipment in 15 years will be $25,736