If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1200, then what is the compound interest on the same sum for the same period and at the same rate when interest is compounded annually?

Introduction / Context:
This question links simple interest and compound interest for the same principal, rate, and time. The simple interest value is provided, which can be used to determine the principal. Once the principal is known, the compound interest for the same rate and time can be computed using the standard compound interest formula. This type of problem checks whether a learner can move between simple interest and compound interest calculations smoothly.

Given Data / Assumptions:

• Simple interest SI for 3 years = Rs. 1200.
• Rate of interest r = 5% per annum.
• Time period n = 3 years.
• Interest for the compound interest part is compounded annually.
• We must find the compound interest CI for the same sum, rate, and time.

Concept / Approach:
For simple interest, the formula is SI = (P * r * t) / 100. Using this, we can solve for the principal P. Once P is known, we apply the compound interest amount formula A = P * (1 + r) ^ n with r in decimal form and n in years. Then CI = A - P. This approach uses the simple interest information purely as a stepping stone to obtain the principal, after which the problem becomes a standard compound interest calculation.

Step-by-Step Solution:
Step 1: Use the simple interest formula SI = (P * r * t) / 100. Step 2: Substitute SI = 1200, r = 5, and t = 3: 1200 = (P * 5 * 3) / 100. Step 3: Simplify the denominator: (5 * 3) / 100 = 15 / 100 = 0.15. Step 4: So 1200 = P * 0.15, which gives P = 1200 / 0.15 = 8000. Step 5: Now compute the amount under compound interest with principal 8000, rate 5% per annum, time 3 years: A = 8000 * (1.05) ^ 3. Step 6: Compute (1.05) ^ 2 = 1.1025 and then multiply by 1.05 again to get (1.05) ^ 3 = 1.157625. Step 7: Multiply to get the amount: A = 8000 * 1.157625 = 9261. Step 8: The compound interest is CI = A - P = 9261 - 8000 = 1261.

Verification / Alternative check:
A quick check is to compare simple interest and compound interest. Simple interest over three years at 5% on 8000 is SI = 8000 * 0.05 * 3 = 1200, which is given. Compound interest should be slightly higher than simple interest for the same rate and period because interest itself earns interest. The difference CI - SI = 1261 - 1200 = 61, which is a modest but positive increase, consistent with expectations. The computed compound interest 1261 is therefore reasonable and fits well with the theory of compounding.

Why Other Options Are Wrong:
Rs. 1251 is slightly smaller than the correct value and might come from approximating the cube of 1.05 or truncating decimals too early. Rs. 1271 is slightly larger than the true CI and indicates an overestimation of compounding. Rs. 1281 is further away, reflecting more significant error in the exponent or multiplication. Rs. 1240 is only marginally above the simple interest, which underestimates the impact of compounding over three years. Only Rs. 1261 fits the exact computation using the correct formulas.

Common Pitfalls:
One common mistake is to try to directly adjust the simple interest to get an approximate compound interest value without using the exact formula. Others mistakenly treat the simple interest formula as if it were still valid under compounding, simply increasing the rate or time, which is not correct. Incorrect calculation of (1.05) ^ 3 due to arithmetic slips is another risk. Carefully separating the simple and compound interest stages and performing the exponentiation correctly helps avoid these errors.

Final Answer:
The compound interest on the same sum at 5% per annum for 3 years, given that the simple interest is Rs. 1200, is Rs. 1261, which corresponds to option B.