Points to Remember:
- Depreciation is the decrease in the value of an asset over time.
- Straight-line depreciation and declining balance depreciation are common methods. This problem uses a declining balance method (compound depreciation).
- The formula for compound depreciation is: Future Value = Present Value * (1 – depreciation rate)^number of years
Introduction:
Depreciation is a crucial concept in accounting and finance. It reflects the wear and tear, obsolescence, or other factors that reduce an asset’s value over its useful life. Several methods exist to calculate depreciation, including straight-line, declining balance, and sum-of-the-years’ digits. This question involves calculating the original purchase price of a TV set using the declining balance method, given its depreciated value after a certain period. The problem requires working backward from the future value to find the initial value.
Body:
Understanding the Problem:
The problem provides the following information:
- Depreciation rate: 12% per annum
- Value in January 2021 (Future Value): â¹4,840
- Time elapsed since purchase: 2 years (January 2019 to January 2021)
We need to determine the purchase price (Present Value) in January 2019.
Calculating the Purchase Price:
We can use the formula for compound depreciation:
Future Value = Present Value * (1 – depreciation rate)^number of years
Let’s denote:
- Future Value (FV) = â¹4,840
- Present Value (PV) = x (this is what we need to find)
- Depreciation rate (r) = 12% = 0.12
- Number of years (n) = 2
Substituting the values into the formula:
4840 = x * (1 – 0.12)²
4840 = x * (0.88)²
4840 = x * 0.7744
x = 4840 / 0.7744
x â 6250
Therefore, the purchase price of the TV set in January 2019 was approximately â¹6250.
Verification:
To verify our answer, we can calculate the value after two years of depreciation:
Value after 1 year = 6250 * (1 – 0.12) = 6250 * 0.88 = 5500
Value after 2 years = 5500 * (1 – 0.12) = 5500 * 0.88 = 4840
This matches the given value in January 2021, confirming our calculation.
Conclusion:
By applying the formula for compound depreciation, we determined that the purchase price of the TV set in January 2019 was approximately â¹6250. This calculation demonstrates the practical application of depreciation principles in determining the original cost of an asset given its depreciated value after a specific period. Understanding depreciation is crucial for accurate financial reporting and asset management. Businesses should utilize appropriate depreciation methods based on the nature of their assets and comply with relevant accounting standards to ensure transparency and accuracy in their financial statements. This promotes financial stability and responsible resource management.
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