Compound Interest — Rs. 800 amounts to Rs. 882 at 5% p.a. compound interest. In how many years does this happen?

Introduction / Context:Under annual compounding, the amount after n years is A = P * (1 + r)^n. With P, A, and r known, we solve for n.

Given Data / Assumptions:

• P = Rs. 800.
• A = Rs. 882.
• r = 5% = 0.05 per annum.

Concept / Approach:(1 + 0.05)^n = 882 / 800 = 1.1025. Recognize 1.1025 = (1.05)^2.

Step-by-Step Solution:(1.05)^n = (1.05)^2 ⇒ n = 2 years.

Verification / Alternative check:Compute: 800 * 1.1025 = 882.

Why Other Options Are Wrong:1, 3, 4, 5 years would not yield exactly Rs. 882 at 5% p.a. compounding.

Common Pitfalls:Applying SI or rounding early instead of recognizing the exact power.

Final Answer:2 years