Text Solution Solution : Given:<br>Time Period (t)`=3` years<br>Let the Principal (P) be `Rs.100`<br>Then the Amount (A) will be `Rs.200` as given in the question that the money will be doubled.<br>And let the rate be R.<br>As we know that:<br>`A=P(1+R/100)^t`<br>`therefore 200=100(1+R/100)^3`<br>`200/100=((100+R)/100)^3`<br>`2=((100+R)/100)^3`<br>`root(3)(2)=(100+R)/100`<br>`1.2599=(100+R)/100`<br>`1.2599times100=100+R`<br>`125.99=R+100`<br>`R=125.99-100`<br>`R=25.99%` per annum.<br>Hence, the rate at which sum of money is doubled in `3` years is `25.99%` per annum.
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Formula for Simple Interest - \(SI = \frac{{P \times R \times T}}{{100}}\) Where, P = Principal R = Rate of interest T = Time period Let the required rate of interest be X. According to the question, SI must be equal to 2 × P in order to make the final sum two times the original principal amount after 5 year. \(\therefore {\rm{P}} = {\rm{}}\frac{{{\rm{P}} \times {\rm{X}} \times 5}}{{100}}\) ⇒ X = 20% ∴ Required rate of interest is of 20%.
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