Respuesta :
Answer:
The value of building in 2014 is 0.92 million.
The value of building in 2018 is 0.84 million.
Step-by-step explanation:
Consider the provided information.
An office building worth $1 million when completed in 2010.
That means the first ordered pair is (0, 1)
Here, 1 is the y intercept.
Here, 0 represents the building is 0 year old while 1 is the worth of building i.e 1 million.
It being depreciated linearly over 50 years and the scarp value is $0.
That means the second ordered pair is (50, 0)
Where, 50 represents, the building is 50 year old while 0 is the worth of building i.e 0 million.
Now use the slope formula:
[tex]m = \frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
[tex]m = \frac{(0-1)}{(50-0)}[/tex]
[tex]m = \frac{-1}{50}[/tex]
The slope intercept form is y=mx+c
Where m is slope and c is the y intercept.
We know slope of the line is -1/50 and y intercept is 1.
Thus, the slope intercept form of the line is:
[tex]y= \frac{-1}{50}x+1[/tex]
Where, x is the time(in years) and y is the value of the building(in millions of dollars).
Now we want the book value of the building in 2014.
First find the value of x and substitute it in the above equation of line.
x=2014-2010=4
Substitute the value of x in [tex]y= \frac{-1}{50}x+1[/tex]
[tex]y= \frac{-1}{50}\times 4+1[/tex]
[tex]y= -0.08+1[/tex]
[tex]y= 0.92[/tex]
Thus, the value of building in 2014 is 0.92 million = 920 thousand dollars.
Now find the value in 2018.
First find the value of x and substitute it in the above equation of line.
x=2018-2010=8
Substitute the value of x in [tex]y= \frac{-1}{50}x+1[/tex]
[tex]y= \frac{-1}{50}\times 8+1[/tex]
[tex]y= -0.16+1[/tex]
[tex]y= 0.84[/tex]
Thus, the value of building in 2018 is 0.84 million = 840 thousand dollars.
The book value of the building in 2014 is $920,000.
The book value of the building in 2018 is $840,000.
What is the book value of the building?
The book value of the building is the current worth of the building less accumulated deprecation.
Annual depreciation = (cost of the building - scrap value) /left of the building
(1,000,000 - 0) / 50 = $20,000
Book value in 2014 = 1,000,000 - ($20,000 x 4) = $920,000
Book value in 2018 = 1,000,000 - ($20,000 x 8) = $840,000
To learn more about depreciation, please check: https://brainly.com/question/25552427
