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Question
Find the rate at which a sum of money will become four times the original amount in 2 years, if the interest is compounded half-yearly.
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Solution
Let the rate percent per annum be R.
Then,
\[A = P \left( 1 + R \right)^{2n} \]
\[4P = P \left( 1 + \frac{R}{200} \right)^4 \]
\[ \left( 1 + \frac{R}{200} \right)^4 = 4\]
\[\left( 1 + \frac{R}{200} \right) = 1 . 4142\]
\[\frac{R}{200} = 0 . 4142\]
R = 82 . 84
Thus, the required rate is 82 . 84 %.
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