If the simple interest on a sum of money at 5% per annum for 3 years is Rs. 1,200, then what is the compound interest on the same principal for the same period at the same rate, assuming annual compounding?

Introduction:
This question connects simple interest and compound interest for the same principal, rate, and time. We are given the simple interest earned over 3 years and asked to find the corresponding compound interest at the same rate and period, which requires us to first determine the principal and then apply the compound interest formula.

Given Data / Assumptions:

• Simple interest (SI) for 3 years = Rs. 1,200
• Rate of interest (r) = 5% per annum
• Time (t) = 3 years
• Same principal, same rate, and interest compounded annually for CI

Concept / Approach:
For simple interest, the formula is:
SI = (P * r * t) / 100We can rearrange this to find P. Once we have P, we apply the compound interest amount formula:
A = P * (1 + r/100)^tThen the compound interest is:
CI = A - P

Step-by-Step Solution:
Step 1: Use SI = (P * r * t) / 100.Step 2: Substitute SI = 1,200, r = 5, and t = 3.Step 3: 1,200 = (P * 5 * 3) / 100 = (15P) / 100.Step 4: Rearrange to find P: P = 1,200 * 100 / 15 = 8,000.Step 5: Apply the compound amount formula: A = 8,000 * (1 + 5/100)^3 = 8,000 * (1.05)^3.Step 6: Compute (1.05)^3 = 1.157625.Step 7: So A = 8,000 * 1.157625 = 9,261.Step 8: Compound interest CI = A - P = 9,261 - 8,000 = 1,261.Thus, the compound interest is Rs. 1,261.

Verification / Alternative check:
We can verify by computing interest year by year: Year 1 interest = 5% of 8,000 = 400, new amount = 8,400. Year 2 interest = 5% of 8,400 = 420, new amount = 8,820. Year 3 interest = 5% of 8,820 = 441, new amount = 9,261. Total compound interest = 400 + 420 + 441 = 1,261, agreeing with the formula result.

Why Other Options Are Wrong:
Rs. 1,251 and Rs. 1,271 are close but correspond to slight miscalculations in (1.05)^3 or rounding errors. Rs. 1,281 is higher than the correct total and comes from adding an extra incorrect interest component. Rs. 1,240 is too low and does not reflect the compounding effect accurately.

Common Pitfalls:
One common error is to treat compound interest as simple interest, leading to SI = Rs. 1,200 being used as if it were CI. Another is miscomputing (1.05)^3 or rounding prematurely. Always compute the principal accurately using the simple interest formula and then use the full compound interest formula with correct exponents.

Final Answer:
The compound interest on the same sum for 3 years at 5% per annum is Rs. 1,261.