At what annual rate of compound interest, compounded annually, will a sum of Rs. 1,200 become Rs. 1,348.32 in 2 years?

Introduction / Context:
Here you must find the compound interest rate that turns a given principal into a known amount over 2 years. This is a typical reverse compound interest problem, where time and both principal and final amount are given, and the rate is unknown.

Given Data / Assumptions:

Principal P = Rs. 1,200.
Amount after 2 years A = Rs. 1,348.32.
Time t = 2 years.
Compounding is annual.
We need to find the annual rate of compound interest r%.

Concept / Approach:
For annual compounding: A = P * (1 + r/100)^t. Here t = 2, so: A / P = (1 + r/100)^2. We can compute the ratio A / P, take the square root to find (1 + r/100), then subtract 1 and convert to a percentage.

Step-by-Step Solution:
Step 1: Compute A / P. A / P = 1,348.32 / 1,200. A / P = 1.1236. Step 2: Relate this to the rate. (1 + r/100)^2 = 1.1236. Take the square root: 1 + r/100 = √1.1236 ≈ 1.06. Step 3: Solve for r. 1 + r/100 ≈ 1.06 → r/100 ≈ 0.06 → r ≈ 6%.

Verification / Alternative check:
Check the obtained rate by recomputing the amount. With r = 6%: A = 1,200 * (1.06)^2 = 1,200 * 1.1236 = Rs. 1,348.32. This matches the given amount exactly, confirming that 6% per annum is the correct compound interest rate.

Why Other Options Are Wrong:
At 5.5%, the factor is (1.055)^2 ≈ 1.1130, giving an amount lower than 1,348.32. At 6.5% or 7%, the factors (1.065)^2 and (1.07)^2 would yield amounts higher than the target. Only 6% gives the precise final amount specified.

Common Pitfalls:
Some candidates mistakenly divide the total percentage increase by two, treating the growth as simple interest. Others forget to take the square root when solving (1 + r/100)^2. Always use the correct compound interest relation and algebraic steps when solving for the rate.

Final Answer:
The required annual compound interest rate is 6% per annum.