Question

An office building worth $1 million when completed in 2010 is being depreciated linearly over 50 years. What was the book value of the building in 2014? What will it be in 20187 (Assume the scrap value is $0.) 2014 2018 5 Need Help? Read w Submit Answer Practice Another Version

Answer 1

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:  

$m = \frac{(y_2-y_1)}{(x_2-x_1)}$

$m = \frac{(0-1)}{(50-0)}$

$m = \frac{-1}{50}$

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:

$y= \frac{-1}{50}x+1$

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 $y= \frac{-1}{50}x+1$

$y= \frac{-1}{50}\times 4+1$

$y= -0.08+1$

$y= 0.92$

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 $y= \frac{-1}{50}x+1$

$y= \frac{-1}{50}\times 8+1$

$y= -0.16+1$

$y= 0.84$

Thus, the value of building in 2018 is 0.84 million = 840 thousand dollars.