Find the amount to be received after $2$ years $6$ months at the rate of $5\%$ p.a. of simple interest on a sum of ₹ $3200$.

### Concept & Simple Interest Amount The total amount received is the sum of the original principal and the simple interest accumulated over the given time period. Time must be converted into years before applying the formula. $$ \text{Amount} = P + \frac{P \times R \times T}{100} $$ ### Step-by-Step Solution - Given: Principal ($P$) = ₹ $3200$, Rate ($R$) = $5\%$ p.a. - Time ($T$) = $2$ years $6$ months = $2 + \frac{6}{12}$ years = $2.5$ years = $\frac{5}{2}$ years. - Calculate the Simple Interest (SI): - $SI = \frac{3200 \times 5 \times 2.5}{100}$ - $SI = 32 \times 12.5$ - $SI = 400$ - Calculate the Total Amount: - $\text{Amount} = P + SI = 3200 + 400 = 3600$ ### Exam Strategy & Shortcut Instead of calculating interest separately, you can calculate the total amount multiplier directly. Total interest percentage = $R \times T = 5\% \times 2.5 = 12.5\%$. Amount = Principal + $12.5\%$ of Principal = $112.5\%$ of $3200$. $112.5\% = \frac{112.5}{100} = \frac{9}{8}$. Amount = $3200 \times \frac{9}{8} = 400 \times 9 = 3600$. ### Common Pitfall Failing to convert months into a fraction of a year (e.g., using $T = 2.6$ instead of $2.5$). ### Final Answer Therefore, the correct answer is **₹ 3600**.