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Question
The difference in simple interest and compound interest on a certain sum of money at \[6\frac{2}{3} %\] per annum for 3 years is Rs 46. Determine the sum.
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Solution
Given:
CI - SI = 46
\[P\left[ \left( 1 + \frac{R}{100} \right)^n - 1 \right] - \frac{PRT}{100} = 46\]
\[P\left[ \left( 1 + \frac{20}{300} \right)^3 - 1 \right] - \frac{P \times 20 \times 3}{3 \times 100} = 46\]
\[\frac{4, 096}{3, 375}P - \frac{P}{5} - P = 46\]
\[\frac{(4, 096 - 3, 375 - 675)P}{3, 375} = 46\]
\[P = 46 \times \frac{3, 375}{46}\]
\[ = 3, 375\]
Thus, the required sum is Rs 3, 375 .
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