At what annual rate of compound interest, compounded once per year, will a sum of Rs. 1,200 amount to Rs. 1,348.32 in 2 years?

Introduction / Context:
This problem involves compound interest, where interest is added to the principal at the end of each compounding period. We are given the initial principal, the final amount after 2 years, and we must find the annual compound interest rate. This tests your ability to manipulate the compound interest formula and solve for the rate.

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 must find the rate of interest per annum (R)

Concept / Approach:
For annual compounding, the compound interest amount is given by:
A = P * (1 + R / 100) ^ TWe substitute A = 1348.32, P = 1200 and T = 2, and then solve for 1 + R / 100. Taking the square root will be required because the exponent is 2.

Step-by-Step Solution:
A = P * (1 + R / 100) ^ 21348.32 = 1200 * (1 + R / 100) ^ 2(1 + R / 100) ^ 2 = 1348.32 / 12001348.32 / 1200 = 1.1236So (1 + R / 100) ^ 2 = 1.1236Take the square root: 1 + R / 100 = sqrt(1.1236)sqrt(1.1236) = 1.06Thus 1 + R / 100 = 1.06R / 100 = 0.06, so R = 6Therefore, the rate of interest is 6% per annum
Verification / Alternative check:
Check by forward calculation. At 6% per annum, the growth factor per year is 1.06. After 2 years, the amount should be:
A = 1200 * (1.06) ^ 2(1.06) ^ 2 = 1.1236A = 1200 * 1.1236 = 1348.32This matches the given final amount exactly, confirming that 6% is correct.

Why Other Options Are Wrong:
At 6.5% the factor would be (1.065) ^ 2 = approximately 1.1342, giving an amount around Rs. 1,361, which is higher than 1,348.32. Rates of 7% and 7.5% give even larger amounts. Hence these rates do not satisfy the given data.

Common Pitfalls:
Candidates sometimes mistakenly use the simple interest formula instead of the compound interest formula. Others forget to take the square root when solving for the rate, or they round incorrectly at intermediate steps. Using exact arithmetic with the ratio 1348.32 / 1200 avoids rounding errors.

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