Comprehension
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?
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 \( \frac{{Cost} - {Scrap Value}}{{Useful Life}} \).
Updated On: Feb 11, 2025
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Solution and Explanation
Step 1: The formula for depreciation using the straight-line method is:
\[
{Depreciation Rate} = \frac{{Cost} - {Scrap Value}}{{Useful Life}}.
\]
Step 2: Substitute the given values:
\[
{Depreciation Rate} = \frac{45200 - 0}{3} = 15066.67 \, {per year}.
\]
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Question: 2
Give a linear equation that describes the computer system's book value at the end of \( t \)th year, where \( 0 \leq t \leq 3 \).
Give a linear equation that describes the computer system's book value at the end of \( t \)th year, where \( 0 \leq t \leq 3 \).
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The book value in the straight-line depreciation method is a linear function, given by \( V(t) = {Initial Cost} - {Depreciation Rate} \times t \).
Updated On: Feb 11, 2025
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Solution and Explanation
Step 1: The book value of the asset decreases over time due to depreciation. The linear equation representing the book value \( V(t) \) at the end of \( t \)th year follows the straight-line method formula:
\[
V(t) = {Initial Cost} - {Depreciation Rate} \times t.
\]
Step 2: Substitute the given values:
\[
V(t) = 45200 - 15066.67t, \quad {where } 0 \leq t \leq 3.
\]
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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?
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 \( V(t) = {Initial Cost} - {Depreciation Rate} \times t \).
Updated On: Feb 11, 2025
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Solution and Explanation
Step 1: Use the linear equation for book value derived earlier:
\[
V(t) = 45200 - 15066.67t.
\]
Step 2: Substitute \( t = 1.5 \) to find the book value after 1.5 years:
\[
V(1.5) = 45200 - 15066.67 \times 1.5.
\]
Step 3: Compute the value:
\[
V(1.5) = 45200 - 22600 = 22600.
\]
Thus, the book value at the end of 1.5 years is ₹ 22,600.
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