If the simple interest on a sum of money at 5% per annum for 3 years is Rs 1200, find the compound interest on the same sum for the same period at the same rate of 5% per annum.

Introduction:
This question connects simple interest and compound interest for the same principal, rate and time period. Using the given simple interest value, you first find the principal and then use the compound interest formula to compute the compound interest for the same conditions.

Given Data / Assumptions:

• Simple interest (SI) for 3 years = Rs 1200.
• Rate of interest (r) = 5% per annum.
• Time (t) = 3 years.
• Same principal and same rate are used for compound interest.
• Compounding is annual for the compound interest calculation.

Concept / Approach:
For simple interest, SI = P * r * t / 100. This allows us to solve for the principal P. Once P is known, we apply the standard compound interest amount formula A = P * (1 + r/100)^t and compute CI = A − P. This systematic approach avoids guesswork and ensures an accurate answer.

Step-by-Step Solution:
Given SI = 1200, r = 5%, t = 3 years.Using SI formula: SI = P * r * t / 1001200 = P * 5 * 3 / 100 = P * 15 / 100So P = 1200 * 100 / 15 = Rs 8000Now compute compound amount for 3 years at 5%:A = P * (1 + 5/100)^3 = 8000 * (1.05)^3(1.05)^2 = 1.1025 and (1.05)^3 ≈ 1.157625A ≈ 8000 * 1.157625 = Rs 9261Compound interest CI = A − P = 9261 − 8000 = Rs 1261

Verification / Alternative Check:
You can also compute compound interest year by year. First year interest: 8000 * 5% = 400 (amount 8400). Second year interest: 8400 * 5% = 420 (amount 8820). Third year interest: 8820 * 5% = 441 (amount 9261). Total CI = 400 + 420 + 441 = 1261, confirming the result.

Why Other Options Are Wrong:
Rs 1251, Rs 1271 and Rs 1281: These values are close but do not match the exact total interest obtained from correct compounding.Rs 1210: This likely arises from confusion with simple interest or from rounding errors.

Common Pitfalls:
A frequent mistake is to use the simple interest formula again for compound interest or to apply the simple interest on the original principal for all three years. Another error is rounding intermediate values too early, which can slightly distort the final answer. Using the amount formula directly helps maintain accuracy.

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