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: Write the rate as a fraction.
A 15% yearly fall means only 85% of the value survives each year, and $85\% = 17/20$. After 8 years the surviving fraction of the original cost is
$$ \left(\frac{17}{20}\right)^8 = \frac{17^8}{20^8} $$

Step 2: Work out the powers.
$17^2 = 289$, so $17^4 = 289^2 = 83521$, and $17^8 = 83521^2 = 6{,}975{,}757{,}441$.
$20^8 = (2 \times 10)^8 = 256 \times 10^8 = 25{,}600{,}000{,}000$.

Step 3: Multiply by the cost and simplify.
$$ SV = 850000 \times \frac{6{,}975{,}757{,}441}{25{,}600{,}000{,}000} $$
The ratio $850000 / 25{,}600{,}000{,}000$ simplifies to $17/512{,}000$, so
$$ SV = \frac{17 \times 6{,}975{,}757{,}441}{512{,}000} = \frac{118{,}587{,}876{,}497}{512{,}000} $$

Step 4: Divide out.
$$ SV = 231616.9463... \text{ Rs.} $$

Step 5: Final answer.
Rounded to the nearest rupee,
$$ \boxed{231617} $$