Find the compound interest on ₹8,000 at 12% per annum for 3 years 4 months, compounded annually.

Question

Find the compound interest on ₹8,000 at 12% per annum for 3 years 4 months, compounded annually.

1. A. ₹3,000
2. B. ₹4,000
3. C. ₹3,689 (Correct answer)
4. D. ₹3,600

Correct Answer

Option C — ₹3,689

Detailed Solution & Explanation

The correct answer is ₹3,689.

Key Points

• For a period of whole years plus a part year, compound the whole years first, then apply simple interest for the fraction.
• Three years: $8000 \times (1.12)^3 = 8000 \times 1.404928 = ₹11{,}239.42$.
• Four months is $\tfrac{1}{3}$ year: $11{,}239.42 \times 12\% \times \tfrac{1}{3} = ₹449.58$.
• Amount $= ₹11{,}689$, so CI $= 11{,}689 - 8{,}000 = ₹3{,}689$.

Additional Information

• The convention matters: for the part year the interest is simple, computed on the amount already accumulated.
• The question asks for the interest, not the amount — subtracting the principal is the final step people forget.
• $(1.12)^3 = 1.404928$ is worth recognising; the general formula is $A = P(1 + R/100)^t$.

प्रश्न (हिन्दी में)

₹8,000 पर 3 वर्ष 4 माह के लिए 12% वार्षिक दर से वार्षिक संयोजित चक्रवृद्धि ब्याज ज्ञात कीजिए।

1. A. ₹3,000
2. B. ₹4,000
3. C. ₹3,689
4. D. ₹3,600