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The compound interest and the simple interest on a certain sum of money for certain period of time and at the same rate of interest are the same find the time. |
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Answer» \(C.I. = S.I\) ⇒ \(P\left( 1 + \frac R{100}\right)^T - P = \frac{PRT}{100}\) ⇒ \(P \left(\left(1 + \frac R {100}\right)^T - 1 \right) = \frac{PRT}{100}\) ⇒ \(\frac {RT}{100} = \left( 1 + \frac R{100}\right)^T - 1\) ⇒ \(\frac {RT}{100} + 1 = \left(\frac{100 + R}{100}\right) ^T\) ⇒ \(\frac{RT + 100}{100} = \left(\frac {R + 100}{100}\right)^T\) For T = 1, L.H.S = \(\frac{R + 100}{100}\) R.H.S. = \(\frac{R + 100}{100}\) Hence, for after 1 year compound interest will be equal to simple interest. |
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