Question

For a computer lab, a set of furniture has just been purchased at the cost of Rs. 8,50,000. The useful life of this furniture is 8 years. If the annual depreciation rate is 15%, then the salvage value of this furniture (in Rs.) is (rounded off to the nearest integer).

Hint:

Use written down value depreciation: salvage value = cost x (1 - rate)^years, with rate = 0.15 and years = 8.

Answer 1

Correct Answer: 231617

Step 1: Understanding the Question.
Furniture costing Rs. 8,50,000 loses value every year at a fixed rate of 15% of its value at the START of that year, not of the original cost. This is the written down value (declining balance) method of depreciation, the method used whenever a percentage rate of depreciation is quoted directly, and we need the value left after 8 years, its salvage value.

Step 2: Key Formula.
For the written down value method,
\[ SV = P (1 - r)^n \]
where \(P\) is the original cost, \(r\) is the annual depreciation rate as a decimal, and \(n\) is the number of years.

Step 3: Substitute the values.
\(P = 8{,}50{,}000\), \(r = 0.15\), \(n = 8\).
\[ SV = 850000 \times (0.85)^8 \]
Build up \((0.85)^8\) two steps at a time:
\[ (0.85)^2 = 0.7225 \]
\[ (0.85)^4 = (0.7225)^2 = 0.52200625 \]
\[ (0.85)^8 = (0.52200625)^2 = 0.2724905250390625 \]

Step 4: Multiply by the original cost.
\[ SV = 850000 \times 0.2724905250390625 = 231616.946... \]

Step 5: Round to the nearest integer, and state the Final Answer.
\[ \boxed{SV \approx 231617 \text{ Rs.}} \]