The difference between simple interest and compound interest on Rs. 1200 for one year at 10% per annum, when the compound interest is reckoned half yearly, is equal to how much?

Introduction / Context:
Here we compare simple interest and compound interest for a short period of one year, but the compound interest is calculated half yearly. Even for a single year, half yearly compounding slightly increases the interest, and we must compute exactly how much more it gives compared with simple interest.

Given Data / Assumptions:

• Principal P = Rs. 1200.
• Annual rate r = 10% per annum.
• Time t = 1 year.
• Compound interest is reckoned half yearly, so two compounding periods in one year.
• We must find CI - SI for this one year period.

Concept / Approach:

Simple interest for one year is straightforward: SI = P * r * t / 100. For compound interest with half yearly compounding, we use the periodic rate r / 2 and number of periods 2t. Amount under compound interest is A = P * (1 + r / 2 / 100)^(2t), and CI = A - P. The difference CI - SI is then taken directly.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Rs. 2.50, Rs. 4.00, and Rs. 4.50 are typical distractors arising from arithmetic slips such as using the wrong periodic rate or miscalculating the second half yearly interest. Only Rs. 3.00 matches both the direct and stepwise calculations.

Common Pitfalls:

The main error is to forget that the second half yearly interest is calculated on the increased amount, not on the original principal. Another mistake is to apply the 10% rate twice instead of 5% each half year, which incorrectly doubles the annual rate.

Final Answer:

The difference between compound interest and simple interest is Rs. 3.00.