Discussion

The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?

Answer: D

\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]

The rate \( 6\tfrac{1}{4}\% \) is \( \tfrac{1}{16} \), so the yearly factor is \( \tfrac{17}{16} \).

\[ P \times \left(\frac{17}{16}\right)^{3} = 4913 \]

Since \( 4913 = 17^{3} \):

\[ P = 4913 \times \frac{16^{3}}{17^{3}} = \frac{17^{3} \times 4096}{17^{3}} = \text{Rs. } 4096 \]

Recognising 4913 as \( 17^{3} \) and 4096 as \( 16^{3} \) turns the whole problem into a single cancellation.

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