Question

At what rate of interest, will a sum of money triple itself in 10 years?

Answer 1

Hint: We shall consider the sum of money invested as x rupees. We have been provided that it gets treble after 3 years which means it becomes 3x. Now, we know that the \[\text{Final}\,\text{amount}=\,\text{Principle}\,\text{amount}+\text{simple}\,\text{interest}\], we will find the simile interest from that and using the formula, \[\text{Simple Interest}=\dfrac{\text{Principle}\,\text{amount}\times \text{time}\times \text{rate}}{100}\], we will find the rate of interest.

Complete step by step solution:
The time period is indicated as 10 years, and the sum triples after 10 years. So, let's start with a sum of money invested of Rs. X. We've been told that in 16 years, it will triple, so,
Final amount \[=3\times x=3x\]
We now know that the total amount is equal to the sum of the principal and simple interest,
\[\text{Final}\,\text{amount}=\,\text{Principle}\,\text{amount}+\text{simple}\,\text{interest}\] which can be written as,
\[3x=\,x+\text{simple}\,\text{interest}\] so, we get the simple interest as\[=3x-x=2x\].
Now, we have the principal amount, time and simple interest, so we will find the rate using the formula, \[\text{Simple Interest}=\dfrac{\text{Principle}\,\text{amount}\times \text{time}\times \text{rate}}{100}\]. So, by substituting the values of the parameters we get,
\[2x=\dfrac{x\times 10\times rate}{100}\]
Now, in this above equation x gets cancelled on both sides we get:
\[\Rightarrow \dfrac{2}{1}=\dfrac{1\times 10\times rate}{100}\]
On cross multiplying, we get,
\[rate=\dfrac{2\times 100}{10}\]
By simplifying further, we get:
\[\Rightarrow rate=20\%\]
So, the correct answer is “\[20\%\]”.

Note: It's possible that pupils believe that simple interest is three times the principal amount, or that simple interest is 3x. As a result, when performing further computations to determine the rate of interest, they will end up with, \[rate=\dfrac{3\times 100}{10}\Rightarrow 30\%\]. However, students should read the question carefully to comprehend that the sum triples after 10 years, implying that the primary amount triples.