Question

Alfred purchased a certain model of car for $26,000 that is known to depreciate 15% annually. What will the value of the car be in 7 years? When will the value of the car be approximately $13,572?

Answer 1

$8,335.

4 years.

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
`FV = PV(1+(r)/(100) )^n`

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.

`FV = PV(1+(r)/(100) )^n`

`FV = 26,000(1+(-15)/(100) )^7`

`FV = 26,000(1-(15)/(100) )^7`

`FV = 26,000(1-0.15)^7`

`FV = 26,000(0.85)^7`

`FV = 26,000(0.32057708828)`

`FV = 8335.00`

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.