The compound interest on a sum at 18% p.a. for 1½ years, compounded yearly, is ₹2,862. Find the principal.

Question

The compound interest on a sum at 18% p.a. for 1½ years, compounded yearly, is ₹2,862. Find the principal.

1. A. ₹10,000 (Correct answer)
2. B. ₹8,000
3. C. ₹2,000
4. D. ₹4,000

Correct Answer

Option A — ₹10,000

Detailed Solution & Explanation

The correct answer is ₹10,000.

Key Points

• For 1½ years compounded yearly, interest compounds once for the full year and then simple interest applies for the half year:
  • Amount = P × (1 + 0.18) × (1 + 0.09), since half of 18% is 9%
  • = P × 1.18 × 1.09 = 1.2862 P
• Compound interest = 1.2862P − P = 0.2862 P.
• Setting 0.2862P = 2,862 gives P = ₹10,000.

Additional Information

• The half-year is charged at half the annual rate when compounding is yearly — this is the standard convention for fractional periods and is exactly what the question tests.
• Had compounding been half-yearly throughout, the rate would be 9% per period over three periods: P(1.09)³, giving a different answer.
• General formulae: A = P(1 + R/100)ⁿ; for half-yearly compounding use rate R/2 over 2n periods, and for quarterly R/4 over 4n.

प्रश्न (हिन्दी में)

किसी धनराशि पर 18% प्रति वर्ष की दर से 1½ वर्ष का चक्रवृद्धि ब्याज, जो वार्षिक रूप से संयोजित होता है, ₹2,862 है। मूलधन ज्ञात कीजिए।

1. A. ₹10,000
2. B. ₹8,000
3. C. ₹2,000
4. D. ₹4,000