Question

In what time will $Rs\,5000$ amount to $Rs\,5750$, if simple interest is reckoned at $7\dfrac{1}{2}\% $ per annum.

Answer 1

Hint: The problem can be solved easily with the concept of simple interest. Interest is the amount of money gained on the principal over a certain period of time.
The problem can be solved easily with the concept of simple interest. Interest is the amount of money gained on the principal over a certain period of time. In simple interest, the principal amount over which the interest is calculated remains the same over time. We will substitute the values of the known quantities into the formula for simple interest to find the time duration.

Complete step by step answer:
In the given problem,
Principal $ = P = Rs\,5000$
Rate of interest $ = 7\dfrac{1}{2}\% $
Converting the interest rate into decimal, we get, $R = 7.5\% $
Time Duration $ = T$
Also, the amount $ = Rs\,5750$
Now, we get the simple interest as $Interest = Amount - principal$.
So, we have the Simple interest as $Rs5750 - Rs5000 = Rs750$.
Now, we know the formula for simple interest earned over the principal amount P over the time period T at rate of interest R as: $Interest = \dfrac{{P \times R \times T}}{{100}}$.
So, substituting the value of known quantities such as principal, rate of interest, and amount, we get,
$Rs750 = \dfrac{{Rs5000 \times 7.5 \times T}}{{100}}$
Shifting the terms in the equation and simplifying the calculations, we get,
$ \Rightarrow \dfrac{{750 \times 100}}{{5000 \times 7.5}} = T$
Cancelling common factors in numerator and denominator, we get,
$ \Rightarrow T = \dfrac{{75}}{{5 \times 7.5}} = \dfrac{{10}}{5}$
$ \Rightarrow T = 2$
So, the time taken by principal amount of $Rs\,5000$ to amount to $Rs\,5750$ at $7\dfrac{1}{2}\% $ per annum is two years.

Note:
In case of compound interest, the principal amount over which the interest is calculated keeps on increasing with time period. Whereas, in simple interest, the principal amount remains constant.
The given problem can also be solved by first finding out $7\dfrac{1}{2}\% $ of the principal amount and then observing the multiples of the simple interest.
$7\dfrac{1}{2}\% $ of principal amount $Rs\,5000$ is $\dfrac{{7.5}}{{100}} \times Rs\,5000 = Rs\,375$
This is the interest earned over one year.
Now, we know that the interest earned over the principal amount is $Rs\,5750 - Rs5000 = Rs750$.
So, we observe the multiples of the interest earned in a year that equals total interest.
We know that \[Rs\,375 \times 1 = Rs\,750\]. Since the second multiple of $Rs\,375$ equals to \[Rs\,750\]. Hence, it will take two years for $Rs\,5000$ amount to $Rs\,5750$, if simple interest is reckoned at $7\dfrac{1}{2}\% $.