The value of a product depreciates at the rate of 10% per annum. If its…
2019
The value of a product depreciates at the rate of 10% per annum. If its present value is ₹ 1,50,000, what will be its worth after 3 years?
Answer: C. 1,09,350 — Concept: When a quantity decreases by a fixed percentage every year (compound depreciation), its value after n years equals the initial value multiplied by (1…
- A.
1,09,250
- B.
1,10,000
- C.
1,09,350
- D.
1,15,500
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Correct answer: C
Concept: When a quantity decreases by a fixed percentage every year (compound depreciation), its value after n years equals the initial value multiplied by (1 − r/100) raised to the power n — each year's cut applies to the previous year's already-reduced balance, not to the original amount.
Applying it here:
Yearly rate of decrease = 10%, so the retention factor kept each year = 1 − 0.10 = 0.9.
Over 3 years, value = 150000 × 0.93.
0.93 = 0.9 × 0.9 × 0.9 = 0.729.
150000 × 0.729 = 109350.
Cross-check:
Year 1: 150000 × 0.9 = 135000.
Year 2: 135000 × 0.9 = 121500.
Year 3: 121500 × 0.9 = 109350 — the same result, confirming the compounding.
Answer: The product's value after 3 years is ₹1,09,350.