A recent accounting graduate opened a new business and installed a computer system that costs ₹ 45,200. The computer system will be depreciated linearly over 3 years and will have a scrap value of ₹ 0.
Question: 1
What is the rate of depreciation?
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The straight-line method of depreciation assumes a fixed amount of depreciation each year, calculated as \( \frac{{Cost} - {Scrap Value}}{{Useful Life}} \).
Step 1: Asset book value declines annually through depreciation. The book value \( V(t) \) after \( t \) years is calculated using the straight-line depreciation formula: \[V(t) = {Initial Cost} - {Depreciation Rate} \times t.\] Step 2: Inputting the provided figures: \[V(t) = 45200 - 15066.67t, \quad {for } 0 \leq t \leq 3.\]
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Question: 3
What will be the computer system's book value at the end of the first year and a half?
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To find the book value at any time \( t \), use the depreciation equation \( V(t) = {Initial Cost} - {Depreciation Rate} \times t \).
Step 1: The book value is calculated using the linear equation: \[V(t) = 45200 - 15066.67t.\] Step 2: To find the book value at 1.5 years, substitute \( t = 1.5 \): \[V(1.5) = 45200 - 15066.67 \times 1.5.\] Step 3: Perform the calculation: \[V(1.5) = 45200 - 22600 = 22600.\] The book value after 1.5 years is ₹ 22,600.
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