At what rate of simple interest per annum will a sum triple itself in 16 years?

We are being asked to find an interest rate for an investment that you want to triple in five years if it is compounded annually. The amount after two years is equal to a subzero, so we need to use our compound interest formula. The initial amount times the quantity of one and R. In this case, we're told to triple our investment. Suppose we started with $100. If it were a triple it would be 300. That would be the case in this case a. 300 would be a sub zero, 100 would be a T. That's the number of times it's compounded and because it's compounded annually, that's a single time. We want this to happen in five years and we are going to raise this to the end. The fifth power. I'm going to divide both sides by 100 to solve this equation. 300 is divided by 100. It's equal to one plus well and divided by one, which is five. I'm going to take the fifth root of our equation and get rid of our exponents. I'm not going to write that down right now. We have the fifth through the three equal to one and R. We're going to do the fifth root of three and subtract one. You'll find that it is approximately 0.2457. That's our value, that's what we have. R is equal to the interest rate when you substitute r into this formula, and the percent is a decimal. The rate would be approximately 25% if you went from the decimal to the%. We know the rate.

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Answer

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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.

In what time will a sum of money treble itself at 16 pa at simple interest?

A sum of money triple itself at 16% p.a. at simple interest in 12.5 years.

At what rate per cent per annum will a sum triple itself in 15 years?

R=12. 5%

At what rate of simple interest per annum will a sum triple itself in 8 years?

Answer: 25% is the rate of interest when principal amount triples in 8 years.

At what rate of simple interest will a sum treble itself in 20 years?

Hence, rate of interest is 10%.