Answer  Hint: We will assume the sum invested as x rupees. We have been given that it becomes triple after 3 years which means it becomes 3 x. Now, we know that the final amount = principal amount + simple interest. So, we will find the simple interest from that and using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$, we will find the rate of interest. Complete step-by-step answer: We are given the time period as 16 years and that the sum becomes triple after 16 years. So, we will first assume the sum invested as Rs. x. We have been given that after 16 years, it becomes triple, so,Final amount = $3\times x=3x$.Now, we know that the final amount is the summation of the principal amount and simple interest,Final amount = principal amount + simple interest, which can be written as,3 x = x + simple interest, so we get the simple interest as = 3 x - x = 2 x.Now, we have the principal amount, time and the simple interest, so we will find the rate using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$. So, by substituting the values of the parameters we get,$\begin{align} & \dfrac{2x}{1}=\dfrac{x\times 16\times rate}{100} \\ & \Rightarrow \dfrac{2}{1}=\dfrac{16\times rate}{100} \\ \end{align}$ On cross-multiplying, we get,$\begin{align} & rate=\dfrac{2\times 100}{16} \\ & \Rightarrow rate=12.5\% \\ \end{align}$ Hence, we get the rate of interest as 12.5 %.Note: There is a possibility that the students think that the simple interest becomes triple of the principal amount, that is simple interest is 3 x. So, in further calculations for finding the rate of interest, they will end up with, $rate=\dfrac{3\times 100}{16}\Rightarrow 18.75\%$. But students should read the question carefully to understand that the sum becomes triple, which means the principal amount becomes triple after 16 years.
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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 three times the original principal amount after 12 year. \(\begin{array}{l} \Rightarrow 2{\rm{P}} = {\rm{\;}}\frac{{{\rm{P\;}} \times {\rm{X\;}} \times 12}}{{100}}\\ \Rightarrow 2 = {\rm{\;}}\frac{{\rm{12X}}}{{100}} \end{array}\) ⇒ X = 50/3% ∴ Required rate of interest is of 50/3%India’s #1 Learning Platform Start Complete Exam Preparation
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At what rate percent per annum will a sum triple itself in 12 years?
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