The difference between simple interest and compound interest on ₹ 1200 for one year at 10% per annum reckoned half-yearly is

### Concept & Formula When interest is reckoned half-yearly, the rate is halved, and the time period is doubled. The standard formula for the difference between C.I. and S.I. for $2$ periods (half-years in this case) is: $$Difference = P \times \left(\frac{R}{100}\right)^2$$ ### Step-by-Step Solution * Given Principal $P = 1200$ * Original Rate $= 10\%$ per annum $\implies$ Half-yearly Rate $R = 5\%$ per half-year * Original Time $= 1$ year $\implies$ Number of periods $n = 2$ half-years * Applying the formula: Difference $= 1200 \times \left(\frac{5}{100}\right)^2$ Difference $= 1200 \times \left(\frac{1}{20}\right)^2$ Difference $= 1200 \times \frac{1}{400}$ Difference $= 3$ ### Exam Strategy & Shortcut Convert the rate and time to their half-yearly equivalents first. Notice that $5\% = \frac{1}{20}$, so squaring it gives $\frac{1}{400}$. The calculation simply becomes $1200 / 400 = 3$, taking only a few seconds. ### Common Pitfall A frequent error is using the annual rate ($10\%$) or treating the time as $1$ period when applying the formula, neglecting the "reckoned half-yearly" condition. ### Final Answer Therefore, the correct answer is **₹ 3**.