An office building worth $1 million when completed in 2005 is being depreciated linearly over 50 years. What will be the book value of the building in 2008? In 2015? (Assume the scrap value is $0.)
in 2008  $  
in 2015  $ 

The office building is depreciated linearly, which means its value decreases at a constant rate every year. We can calculate the rate of depreciation and then use it to determine the book value at specific years.

### Step 1: Calculate the annual depreciation
Since the building is depreciated over 50 years and its original value is $1 million, the annual depreciation is:
\[
\text{Annual Depreciation} = \frac{\text{Initial Value}}{\text{Years}} = \frac{1,000,000}{50} = 20,000 \text{ dollars per year.}
\]

### Step 2: Calculate the book value in 2008
From 2005 to 2008 is 3 years. So, the total depreciation by 2008 is:
\[
\text{Depreciation by 2008} = 20,000 \times 3 = 60,000 \text{ dollars.}
\]
The book value in 2008 is:
\[
\text{Book Value in 2008} = 1,000,000 - 60,000 = 940,000 \text{ dollars.}
\]

### Step 3: Calculate the book value in 2015
From 2005 to 2015 is 10 years. So, the total depreciation by 2015 is:
\[
\text{Depreciation by 2015} = 20,000 \times 10 = 200,000 \text{ dollars.}
\]
The book value in 2015 is:
\[
\text{Book Value in 2015} = 1,000,000 - 200,000 = 800,000 \text{ dollars.}
\]

### Final Answer:
- In 2008: **$940,000**
- In 2015: **$800,000**

Would you like further clarification or details on any part of this? Here are five follow-up questions you might consider:

1. How would the calculation change if the scrap value was not zero?
2. What happens if the depreciation is not linear but exponential?
3. How do you calculate the book value after 25 years?
4. What is the book value in 2030 using the same linear depreciation method?
5. What is the impact of inflation on the real value of the building?

**Tip:** When calculating depreciation, always double-check the timeline to ensure the correct number of years is used.

An office building worth $1 million when completed in 2005 is being depreciated linearly over 50 years. What will be the book value of the building in 2008? In 2015? (Assume the scrap value is $0.)

Calculate the book value of an office building worth $1 million, depreciated linearly over 50 years. Find the value in 2008 and 2015 using simple arithmetic and depreciation formulas. Suitable for high school students (Grades 9-12).

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