An automobile purchased for use by the manager of a firm at a price of $33,000 is to be depreciated by using the straight-line method over 5 years. What will be the book value of the automobile at the end of 2 years? (Assume that the scrap value is $0.)

To calculate the book value of the automobile at the end of 2 years using the straight-line depreciation method, we need to follow these steps:

### Step 1: Calculate the Annual Depreciation Expense

The **straight-line depreciation** method spreads the cost of the asset evenly over its useful life. The formula for the annual depreciation expense is:

\[
\text{Annual Depreciation Expense} = \frac{\text{Cost of the Asset} - \text{Scrap Value}}{\text{Useful Life}}
\]

Given:
- Cost of the automobile (initial value) = $33,000
- Scrap value = $0
- Useful life = 5 years

\[
\text{Annual Depreciation Expense} = \frac{33,000 - 0}{5} = \frac{33,000}{5} = 6,600
\]

### Step 2: Calculate the Depreciation Over 2 Years

To find the total depreciation after 2 years:

\[
\text{Depreciation After 2 Years} = \text{Annual Depreciation Expense} \times 2 = 6,600 \times 2 = 13,200
\]

### Step 3: Calculate the Book Value at the End of 2 Years

The **book value** of the automobile at the end of 2 years is the initial cost minus the accumulated depreciation over those 2 years:

\[
\text{Book Value After 2 Years} = \text{Initial Cost} - \text{Depreciation After 2 Years}
\]

\[
\text{Book Value After 2 Years} = 33,000 - 13,200 = 19,800
\]

### Conclusion

The book value of the automobile at the end of 2 years is **$19,800**.

Would you like more details on this topic, or do you have any questions? 

Here are some related questions for further exploration:
1. How would the depreciation be calculated if the scrap value were not zero?
2. What is the difference between straight-line and declining balance depreciation methods?
3. How does changing the useful life of an asset affect the depreciation expense?
4. What are some common assets that are depreciated using the straight-line method?
5. How is depreciation accounted for in financial statements?

**Tip:** Depreciation helps companies allocate the cost of an asset over its useful life, giving a more accurate representation of the asset's value over time.

Learn how to calculate the book value of an automobile after 2 years using the straight-line depreciation method. This problem covers essential concepts in accounting and finance, including depreciation calculations and book value determination. Suitable for students in Grades 10-12.

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