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:
[tex]FV=P(1-r)^t[/tex]
Substituting the given data:
[tex]FV=\$21,100(1-0.152)^5[/tex]
Calculating:
[tex]\begin{gathered} FV=\$21,100(0.848)^5 \\ FV=\$21,100\cdot0.4385 \\ FV=\$9,252.56 \end{gathered}[/tex]
As you can see, both models produce very different results.
