At what rate percent per annum simple interest will a sum treble itself in 8 years

Answer

At what rate percent per annum simple interest will a sum treble itself in 8 years
Verified

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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At what rate percent per annum simple interest will a sum treble itself in 8 years

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Updated On: 27-06-2022

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At what rate percent per annum simple interest will a sum treble itself in 8 years

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At what rate percent per annum will a sum treble itself in 8 years?

⇒R=2P×100P×16=12.5%

At what rate percent per annum simple interest will a sum double itself in 8 years?

Hence, the rate of interest to double a money in 8 years will be 12.5% per annum.

In what time the sum of money will triple at 8% pa simple interest?

This is Expert Verified Answer hence, after 25 years sum of money will be triple itself .

At what rate percent per annum will a sum treble itself in 10 years?

Hence, we get the rate of interest as 12.5 %.