At what rate percent per annum of compound interest will a sum of money become four times of itself in two years?

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.

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 %.

Concept: Rate Compounded Annually Or Half Yearly (Semi Annually)

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At what rate per cent compound...

Updated On: 27-06-2022

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