Question

Linda 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 five years, how much will it be worth in two years.

Answer 1

The value at the end of year 2 is $4400.

Explanation:

The best approach here is to determine the expression for the line depreciation and then calculate the depreciation value at x = 2 years.

A line is given by

`y = mx + b`

where m is the slope and b the bias (aka y-intercept). You can determine both directly from what is given. The slope is change in y divided by change in x. We know that over 5 years the car loses (500-7000)=-6500 in value. So, the slope is m=-6500/5 (note the negative sign). At time 0, the y-intercept is 7000, since that is the initial value (at year 0). So our line function is fully identified:

`y = -(6500)/(5)x+7000`

and gives you the value of the car in any given year. To answer the question, we now plug in 2 as value of x:

`y=-(6500)/(5)\cdot 2 + 7000= 4400`