Compound Interest – Find time from interest earned: On ₹ 30,000 at 7% per annum compound interest, the total compound interest is ₹ 4,347. Find the time in years (annual compounding).

Introduction / Context:Given principal, rate, and compound interest earned, we can infer the time by comparing amount factors (1 + r)^t.

Given Data / Assumptions:

• P = ₹ 30,000
• r = 7% per annum
• Compound interest (CI) = ₹ 4,347
• Compounding yearly

Concept / Approach:CI = A − P, so A = P + CI = 304347. Compare A/P to (1 + r)^t to solve for t.

Step-by-Step Solution:A = 30000 + 4347 = 34347A/P = 34347 / 30000 = 1.1449(1 + 0.07)^2 = 1.1449 → t = 2 years

Verification / Alternative check:Direct CI for 2 years: P[(1.07)^2 − 1] = 30000(1.1449 − 1) = 30000 * 0.1449 = 4347 (matches).

Why Other Options Are Wrong:2.5, 3, 4 years give factors higher than 1.1449 at 7%.

Common Pitfalls:Using simple interest 2 * 7% = 14% (which would give 4200, not 4347).

Final Answer:2 yr