What would be the compound interest accrued on an amount of ₹ 8400 @ 12.5 p.c.p.a. at the end of 3 years?

### Concept & Fractional Rates When the rate of interest is a standard fraction (like $12.5\% = \frac{1}{8}$), converting the percentage to a fraction simplifies the calculation of the amount significantly. $$ A = P(1 + \frac{1}{8})^n $$ ### Step-by-Step Solution * **Given:** Principal ($P$) = ₹ 8400, Rate ($R$) = $12.5\% = \frac{1}{8}$, Time ($n$) = 3 years. * **Step 1:** Set up the amount equation using the fraction. $A = 8400 \times (1 + \frac{1}{8})^3$ $A = 8400 \times (\frac{9}{8})^3$ * **Step 2:** Expand the calculation. $A = 8400 \times \frac{729}{512}$ * **Step 3:** Simplify the multiplication. $A = \frac{8400}{512} \times 729 = 16.40625 \times 729$ $A = 11960.15625$ * **Step 4:** Calculate Compound Interest. $CI = A - P = 11960.15625 - 8400 = 3560.15625$ * **Step 5:** Round to two decimal places (standard for currency). $CI \approx 3560.16$ ### Exam Strategy & Shortcut Use digital sum or approximation if the options are far apart. However, since the options are precise and contain decimals, exact calculation using the fractional equivalent $\frac{1}{8} \rightarrow \frac{9}{8}$ is the most structured approach. ### Common Pitfall Trying to calculate $(1.125)^3$ via standard decimal multiplication takes far too much time and increases the risk of arithmetic errors compared to using fractions. ### Final Answer Therefore, the correct answer is **₹ 3560.16**.