The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is

Question

The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is

1. A. 2.5
2. B. 2 (Correct answer)
3. C. 5
4. D. 4

Correct Answer

Option B — 2

Detailed Solution & Explanation

The correct answer is 2.

Key Points

• Compound interest is the amount minus the principal:
  • $CI = P(1 + r)^n - P$
• Substituting $P = 30{,}000$, $r = 7\% = 0.07$ and $CI = 4{,}347$:
  • $30000(1.07)^n - 30000 = 4347$
  • $30000(1.07)^n = 34347$
  • $(1.07)^n = \frac{34347}{30000} = 1.1449$
• Since $(1.07)^2 = 1.1449$, we get $n = \mathbf{2}$ years.

Shortcut Trick

• Test the smallest option first rather than solving for $n$:
  • Year 1 interest $= 7\%$ of $30{,}000 = 2{,}100$ → amount $32{,}100$
  • Year 2 interest $= 7\%$ of $32{,}100 = 2{,}247$ → total CI $= 2100 + 2247 = 4{,}347$ ✓
• Two lines of simple percentage work beat any logarithm here.

Additional Information

• Recognising 1.1449 is worth doing on sight — it is $1.07^2$. Similarly useful squares: $1.05^2 = 1.1025$, $1.06^2 = 1.1236$, $1.10^2 = 1.21$.
• Sanity check for CI questions: simple interest for 2 years would be $2 \times 2100 = 4{,}200$. The stated CI of 4,347 is only slightly higher, which is exactly what a 2-year compounding period should produce — a 5-year period would give far more.