Question

What will it’s value be in 5 years if it depreciates 15.2% each year?

Answer 1

Depreciation

The value of a new truck is P=$21,100. The estimated depreciation rate is r=15.2% per year.

We can compute the final value of the truck after t=5 years by using several depreciation models.

• Linear model:

It assumes the original value goes to zero in a given amount of time and the curve from the original value to zero is a straight line.

We can model the future value of the truck as:

FV = P(1 - rt)

Using the given values (r=0.152):

FV = $21,100 (1 - 0.152 * 5)

FV = $21,100 (1 - 0.76)

FV = $21,100 * 0.24

FV = $5,064

• Exponential model

The formula for the future value is:

`FV=P(1-r)^t`

Substituting the given data:

`FV=\$21,100(1-0.152)^5`

Calculating:

`\begin{gathered} FV=\$21,100(0.848)^5 \\ FV=\$21,100\cdot0.4385 \\ FV=\$9,252.56 \end{gathered}`

As you can see, both models produce very different results.