Discussion

What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?

Answer: A

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

The step from year 2 to year 3 gives the rate.

\[ 1 + \frac{R}{100} = \frac{9261}{8820} = 1.05 \quad\Longrightarrow\quad R = 5\% \]

Now work back two years from Rs. 8820:

\[ P = \frac{8820}{(1.05)^{2}} = \frac{8820}{1.1025} = \text{Rs. } 8000 \]

Getting the rate from two consecutive amounts first is what makes the principal a single division away.

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