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Question
At what rate percent per annum will a sum of Rs 4000 yield compound interest of Rs 410 in 2 years?
Solution
Let the rate percent be R.
We know that:
\[CI = P \left( 1 + \frac{R}{100} \right)^n - P\]
\[410 = 4, 000 \left( 1 + \frac{R}{100} \right)^2 - 4, 000\]
\[4, 410 = 4, 000 \left( 1 + \frac{R}{100} \right)^2 \]
\[ \left( 1 + \frac{R}{100} \right)^2 = \frac{4, 410}{4, 000}\]
\[ \left( 1 + \frac{R}{100} \right)^2 = 1 . 1025\]
\[ \left( 1 + \frac{R}{100} \right)^2 = \left( 1 . 05 \right)^2 \]
\[1 + \frac{R}{100} = 1 . 05\]
\[\frac{R}{100} = 0 . 05\]
R = 5
Thus, the required rate percent is 5.
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