Compound Interest — Determine time from total CI on a known principal: The compound interest on ₹ 30000 at 7% per annum for a certain time is ₹ 4347. Find the time (compounded yearly).

Introduction / Context:
Total compound interest equals P[(1 + r)^t − 1]. If P, r, and CI are known, we can solve for t by matching the factor (1 + r)^t to 1 + CI/P. With standard rates and times, this often collapses to recognizing a tabulated power.

Given Data / Assumptions:

• P = ₹ 30000
• r = 7% = 0.07 per year
• CI = ₹ 4347
• Annual compounding; find t

Concept / Approach:
Compute 1 + CI/P = 1 + 4347/30000 = 1 + 0.1449 = 1.1449. Recognize that (1.07)^2 = 1.1449. Therefore, t = 2 years exactly.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Other times do not produce the factor 1.1449 at 7% with annual compounding.

Common Pitfalls:

• Mistaking amount (principal + interest) for “interest only”.

Final Answer:
2 years.