A certain car was purchased for $30,400. The car has a resale value of $26,600 after a useful life of 5 years. What is the book value of this car after 4 years?
Annual depreciation expense = $760
Book value = $ [?]
Round to the nearest hundredth.
Answer (2)
Define the initial cost of the car as $30 , 400 .
Calculate the total depreciation after 4 years: 4 × $760 = $3040 .
Calculate the book value after 4 years by subtracting the total depreciation from the initial cost: $30 , 400 − $3040 = $27 , 360 .
The book value of the car after 4 years is 27360.00 .
Explanation
Understanding the Problem We are given the initial cost of a car, its resale value after 5 years, and the annual depreciation expense. We need to find the book value of the car after 4 years. The book value is the initial cost minus the accumulated depreciation.
Defining Variables The initial cost of the car is C = $30 , 400 . The annual depreciation expense is D = $760 . We want to find the book value after t = 4 years.
Calculating Total Depreciation The total depreciation after 4 years is 4 × D = 4 × $760 = $3040 .
Calculating Book Value The book value after 4 years is the initial cost minus the total depreciation: C − 4 D = $30 , 400 − $3040 = $27 , 360 .
Final Answer Therefore, the book value of the car after 4 years is $27 , 360.00 .
Examples
Understanding book value is essential in accounting and finance. For example, if a company wants to sell an asset like a car, knowing the book value helps determine a fair selling price. If the market value is higher than the book value, the company can sell it for a profit. Conversely, if the market value is lower, the company might need to sell it at a loss. This concept is also crucial for calculating taxes and understanding a company's financial health.
The book value of the car after 4 years is $27,360.00, calculated by subtracting the total depreciation from the initial purchase price of the car. The total depreciation over 4 years is $3,040, which is the annual depreciation multiplied by 4. Thus, the final book value is $30,400 - $3,040 = $27,360.
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