CA Foundation · Quantitative Aptitude · Mathematics of Finance
A machine costing ₹1,00,000 is depreciated by a constant percentage on the written-down value so that its value after 2 years is ₹81,000. What is the rate of depreciation per annum?
The annual rate is 10%. The value falls to 0.81 of cost in two years, and the annual retention factor is the square root of 0.81, which is 0.9. Hence depreciation is 10% of the opening written-down value each year.
- A5%
- B9.5%
- C10%Correct
- D19%
Explanation
(1−r)^2 = 81,000/1,00,000 = 0.81, so 1−r = 0.9 and r = 10%. Option 19% is total depreciation over 2 years, not the annual rate. Option 9.5% is half of 19%, which wrongly averages the total.
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