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Question
Find the rate at which a sum of money will double itself in 3 years, if the interest is compounded annually.
Solution
Let the rate percent per annum be R.
Then,
\[A = P \left( 1 + \frac{R}{100} \right)^n \]
\[2P = P \left( 1 + \frac{R}{100} \right)^3 \]
\[ \left( 1 + \frac{R}{100} \right)^3 = 2\]
\[\left( 1 + \frac{R}{100} \right) = 1 . 2599\]
\[\frac{R}{100} = 0 . 2599\]
R = 25 . 99
Thus, the required rate is 25 . 99 % per annum.
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