Answer:
$8,335.
4 years.
Step-by-step explanation:
There are two ways to find the future value of a car that depreciates.
The first way to find the value is to use the annual depreciation formula [tex]FV = PV(1+\dfrac{r}{100} )^n[/tex]
Let's break down the variables and value that we already have available.
FV = ?
PV = 26,000
r = -15% (We change this to negative because the value is depreciating)
n = 7
Now let's use the formula and substitute all the variables and values that we have.
[tex]FV = PV(1+\dfrac{r}{100} )^n[/tex]
[tex]FV = 26,000(1+\dfrac{-15}{100} )^7[/tex]
[tex]FV = 26,000(1-\dfrac{15}{100} )^7[/tex]
[tex]FV = 26,000(1-0.15)^7[/tex]
[tex]FV = 26,000(0.85)^7[/tex]
[tex]FV = 26,000(0.32057708828)[/tex]
[tex]FV = 8335.00[/tex]
So after 7 years the value will be $8335.00.
Another way is to use a balance sheet to see how much the value will go down.
Please refer to the attached image.
