The principal that amounts to ₹ 4913 in 3 years at $6\frac{1}{4}\%$ per annum compound interest compounded annually, is (S.S.C., 2005)

### Concept & Conversion Converting fractional percentages into standard fractions significantly speeds up compound interest calculations. $6\frac{1}{4}\% = \frac{25}{4}\% = \frac{25}{400} = \frac{1}{16}$ This means the multiplier for each year is $\left(1 + \frac{1}{16}\right) = \frac{17}{16}$. ### Step-by-Step Solution * Given Amount $A = 4913$ * Time $n = 3$ years * Rate $R = 6\frac{1}{4}\% \implies$ Fraction = $\frac{1}{16}$ * Using the formula $A = P \times (\text{Multiplier})^n$: $4913 = P \times \left(\frac{17}{16}\right)^3$ * Expanding the fraction: $4913 = P \times \frac{17 \times 17 \times 17}{16 \times 16 \times 16}$ * Let's calculate $17^3$: $17^2 = 289$ $289 \times 17 = 4913$. * Substitute back into the equation: $4913 = P \times \frac{4913}{4096}$ $P = 4096$ ### Exam Strategy & Shortcut Memorizing cubes up to $20$ is highly recommended for aptitude exams. Recognizing that $4913$ is exactly $17^3$ instantly collapses the equation, requiring only the calculation of $16^3$, which is $4096$. ### Common Pitfall Using decimals ($6.25\%$) leads to $1.0625^3$, an extremely tedious calculation by hand that is highly prone to arithmetic errors. Always use fractions for awkward rates like $6.25\%$, $12.5\%$, $16.66\%$, etc. ### Final Answer Therefore, the correct answer is **₹ 4096**.