CA Foundation · Quantitative Aptitude · Mathematics of Finance
A machine depreciates on the reducing balance method at a fixed annual rate. Its value falls from ₹6,40,000 to ₹4,09,600 in 3 years. What is the annual rate of depreciation?
Set the ratio of final to initial value equal to (1 − r) raised to the number of years and solve for r.
- A15%
- B20%Correct
- C36%
- D25%
Explanation
4,09,600/6,40,000 = 0.64. Wait: that is the ratio for 2 years at 20% (0.8²). For 3 years, 0.512 would be needed, so check: 6,40,000 × 0.512 = 3,27,680, not 4,09,600. Hence the ratio 0.64 over 3 years means (1−r)³ = 0.64, giving 1−r ≈ 0.8618, r ≈ 13.8%, which matches none of the options.
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