Discussion

A sum of money becomes Rs 13,380 in 3 years and Rs 20,070 in 6 years at compound interest. The initial sum is?

Answer: C

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

The same growth factor applies to each three-year stretch, so compare the two amounts.

\[ \frac{20070}{13380} = 1.5 \]

That 1.5 is the three-year multiplier, and it also carries the sum from the start to year 3:

\[ P \times 1.5 = 13380 \quad\Longrightarrow\quad P = \text{Rs. } 8920 \]

The annual rate works out at \( \sqrt[3]{1.5} - 1 = 14.47\% \), but it is never needed - the three-year factor does all the work.

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