Discussion
At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
Answer: A
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
\[ \left(1 + \frac{R}{100}\right)^{2} = \frac{1348.32}{1200} = 1.1236 \]
\[ 1 + \frac{R}{100} = \sqrt{1.1236} = 1.06 \]
\[ R = 6\% \]
Averaging the total growth of 12.36% over two years to get 6.18% is close but wrong; the square root, not the halving, is what inverts two years of compounding.
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