Question

Brent purchased a used vehicle that depreciates under a straight-line method. The initial value of the car is $7500, and the salvage value is $500. If the car is expected to have a useful life of another 7 years, how much will it depreciate each year?

Answer 1

Let the value of the vehicle be described by the equation
V = a + bx
where x =  number of years since purchase
a,b are constants.

When x = 0, V = $7500. Therefore
a + b*0 = 7500
a = 7500

When x = 7, V = $500. Therefore
7500 + 7b = 500
7b = 500 -7500 = -7000
b = -7000/7 = -1000

The equation is
V = 7500 - 1000x

The slope of this equation is the depreciation rate, and it is -$1000 per year.

Answer: $1000 depreciation per year.