SOLUTION: The purchase price for a company car is $19,800. The useful life is 6 years after which it will have an estimated scrap value of $1,200. -Find the linear equation relating book va

Question 1174241: The purchase price for a company car is $19,800. The useful life is 6 years after which it will have an estimated scrap value of $1,200.
-Find the linear equation relating book value and number of years.
- What is the book value after four years?
Show all work.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the price of the car is 19,800.
that's the book value at the end of year 0.
the end of year 0 is the beginning of year 1.
the salvage value at the end of year 6 is 1,200.
that's the book value at the end of year 6.

using straight line depreciation, the formula would be:
y = mx + b
m is the slope
b is the y-intercept
y is the value after x years.
x is the number of years.

when x = 0, y = 19,800.
when x = 6, y = 1,200

to find the slope, you need 2 points on the line.
the first point is (x1,y1) = (0,19800)
the second point is (x2,y2) = (6,1200)

the slope is (y2-y1)/(x2-x1) = (1200 - 19800)/(6-0) = -18600/6 = -3100
the equation becomes y = -3100 * x + b
replace x and y with one of the points to find b.
i used (0,19800)
y = -3100 * x + b becomes 19800 = -3100 * 0 + b
solve for b to get:
b = 19800.
the equation becomes y = -3100 * x + 19800

when x = 0, the equation becomes y = -3100 * 0 + 19800.
solve for y to get y = 19800.
that's the book value at the end of year 0.

when x = 6, the equation becomes y = -3100 * 6 + 19800.
solve for y to get y = 1200.
that's the book value at the end of year 6.

when x = 4, the equation becomes y = -3100 * 4 + 19800.
solve for y to get y = 7400.
that's the book value at the end of year 4.
that's your solution.

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