Question

Find the rate of simple interest when:
$Rs\,300$ amounts to $Rs\,400$ in two years.

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 formula for simple interest gained over a principal amount P at a rate of interest R over time period T is $Simple\,Interest = \dfrac{{P \times R \times T}}{{100}}$. So, we will first calculate the simple interest earned at the principal amount in two years by subtracting the principal amount from the total amount after two years.

Complete answer:
In the given problem,
Principal $ = P = Rs\,300$
Rate of interest $ = R$$\% $
Time Duration $ = 2\,years$
Now, the total amount after two years is given to us as $Rs\,400$.
So, we can calculate the simple interest by subtracting the principal from the total amount.
Hence, simple interest $ = Rs\,400 - Rs\,300$
$ = Rs\,100$
Now, we will substitute the known values into the formula of simple interest to find the rate of interest.
So, we get,
$Simple\,Interest = \dfrac{{P \times R \times T}}{{100}}$
$ \Rightarrow Rs\,100 = \dfrac{{Rs\,300 \times R \times 2}}{{100}}$
Shifting all the constant to the left side of the equation, we get,
$ \Rightarrow \dfrac{{Rs\,100 \times 100}}{{Rs\,300 \times 2}} = R$
Changing the sides of equation and simplifying the calculations, we get,
$ \Rightarrow R = \dfrac{{100 \times 100}}{{300 \times 2}}$
$ \Rightarrow R = \dfrac{{100}}{{3 \times 2}} = \dfrac{{50}}{3}$
$ \Rightarrow R = 16.67\% $
So, the rate of interest is $16.67\% $.

Note:
Total amount is the sum of the simple interest over the principal amount over a specific time period and the principal amount. In simple interest, the interest is gained over the original principal amount only for the entire time period, unlike the case of compound interest where the principal amount is increased after every compounding time period.