The simple interest on a certain sum of money at 5% per annum for 3 years is Rs. 1200. What is the compound interest on the same sum for the same period at the same rate of 5% per annum, compounded annually?

Introduction / Context:
This question connects simple interest and compound interest on the same principal, rate, and time. It checks whether you can first extract the principal from simple interest data and then correctly use the compound interest formula. This is a typical multi-step aptitude question involving interest calculations.

Given Data / Assumptions:

• Simple interest SI = Rs. 1200
• Rate r = 5% per annum
• Time T = 3 years
• Principal P is unknown
• Compound interest is compounded annually at the same rate and for the same period

Concept / Approach:
First, we use the simple interest formula:
SI = P * r * T / 100to find the principal P. Then we use the compound interest amount formula:
A = P * (1 + r / 100)^TFinally, the compound interest CI is:
CI = A - P

Step-by-Step Solution:
Step 1: Find the principal using simple interest.1200 = P * 5 * 3 / 1001200 = P * 15 / 100P = 1200 * 100 / 15 = Rs. 8000Step 2: Compute the amount at compound interest for 3 years.A = 8000 * (1 + 5 / 100)^3A = 8000 * (1.05)^3(1.05)^3 = 1.157625A = 8000 * 1.157625 = Rs. 9261Step 3: Compute compound interest.CI = A - P = 9261 - 8000 = Rs. 1261

Verification / Alternative check:
You can expand year by year: after year 1, amount = 8000 * 1.05 = 8400; after year 2, amount = 8400 * 1.05 = 8820; after year 3, amount = 8820 * 1.05 = 9261. The difference 9261 - 8000 is 1261, which confirms our earlier calculation.

Why Other Options Are Wrong:
Rs. 1251, Rs. 1271, Rs. 1281: These come from incorrect rounding or wrong multiplication of (1.05)^3.Rs. 1240: This is close to the simple interest and indicates confusion between simple and compound interest.

Common Pitfalls:
Common mistakes include using the simple interest formula again for the second part, or forgetting to find the principal first. Another frequent error is computing (1.05)^3 incorrectly or rounding too early in intermediate steps. Always keep sufficient decimal precision until the final step to ensure the correct result.

Final Answer:
The compound interest on the same sum for 3 years at 5% per annum is Rs. 1261.