Question

Thomas purchased a used vehicle that depreciates under a straight-line

method. The initial value of the car is $7000, and the salvage value is $500. If
the car is expected to have a useful life of another 5 years, how much will it
depreciate each year?
O
A. $7000
O
B. $1300
O
O
C. $5000
D. $1000

Answer 1

Option B:

$1300

Solution:

Given initial value = $7000, salvage value = %500, time = 5 years

Let the value of the vehicle be described by the equation

V = a + bx – – – – – (1)

where x = number of years since purchase, a and b are constants.

When x = 0, V = $7000

a + b × 0 = 7000

⇒ a + 0 =7000

⇒ a = 7000

When x = 5, V = $500. Therefore

7000 + 5b = 500

5b = 500 – 7000

5b = –6500

`$b=(-6500)/(5)=1300`

The equation is

V = 7000 – 1300x

The slope of this equation is the depreciation rate.

Here slope is 1300.

Option B is the correct answer.

Hence $1300 depreciation per year.