CA Foundation · Quantitative Aptitude · Mathematics of Finance
A machine costing ₹3,00,000 is depreciated at a constant percentage on the reducing balance method. After 2 years its book value is ₹1,92,000. What is the annual rate of depreciation?
The annual depreciation rate is 20%. The value fell to 1,92,000/3,00,000 = 0.64 of cost in two years, so the yearly retention factor is the square root of 0.64, which is 0.8. Hence depreciation is 20% per year. The 36% figure is the total two-year fall.
- A20%Correct
- B25%
- C36%
- D18%
Explanation
Let rate be r. 3,00,000(1-r)^2 = 1,92,000, so (1-r)^2 = 0.64, and 1-r = 0.8, giving r = 20%. Check: 3,00,000 × 0.8 × 0.8 = 1,92,000. The 36% option is the total two-year fall (1 - 0.64) taken as the annual rate.
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