The compound interest on ₹ 2800 for 18 months at 10% p.a. is

### Concept & Fractional Years For fractional years (like 1.5 years), the interest for the full year is applied fully, and for the remaining fraction of the year, the rate is multiplied by that fraction. $$ A = P(1 + \frac{R}{100})^1 \times (1 + \frac{\frac{1}{2}R}{100}) $$ ### Step-by-Step Solution * **Given:** Principal ($P$) = ₹ 2800, Rate ($R$) = 10% p.a., Time = 18 months = $1 \frac{1}{2}$ years. * **Step 1:** Calculate the multipliers for the time periods. 1st year multiplier: $(1 + \frac{10}{100}) = 1.10$ Next half-year rate: $\frac{10}{2} = 5\%$ Half-year multiplier: $(1 + \frac{5}{100}) = 1.05$ * **Step 2:** Calculate total Amount ($A$). $A = 2800 \times 1.10 \times 1.05$ $A = 2800 \times 1.155$ $A = 3234$ * **Step 3:** Calculate Compound Interest. $CI = A - P = 3234 - 2800 = 434$ ### Exam Strategy & Shortcut Use the successive percentage change formula for 1 year and 0.5 years. The rates are $10\%$ and $5\%$. Equivalent total rate = $10 + 5 + \frac{10 \times 5}{100} = 15.5\%$. Now, simply find $15.5\%$ of 2800. $15.5\% \times 2800 = 15.5 \times 28 = 434$. This takes less than 10 seconds. ### Common Pitfall A common error is treating the time as compounding half-yearly for all 3 cycles (which would mean $r=5\%$, $n=3$). The problem says 10% p.a., so compounding is annual unless stated otherwise, leading to fractional year rules. ### Final Answer Therefore, the correct answer is **₹ 434**.