Question

Find the rate of simple interest for an amount equal to Rs.35,246, Principal Rs.20000 for 5 years.

Answer 1

Hint: In this question, we are given the amount after simple interest, principal amount, and time period. We have to find the rate of simple interest per annum. For this, we will first evaluate simple interest using A = P + SI, where SI is the simple interest, A is the amount after simple interest and P is the principal amount. After that, we will put values of P, T, SI in the formula $SI=\dfrac{P\times R\times T}{100}$ to evaluate R which is the required rate of interest per annum.

Complete step by step solution:
Here, we are given an amount of simple interest as Rs.35,246. We are given principal amount P as Rs.20000 and time period T as 5 years. We need to find the rate of simple interest per annum. So, let us suppose the rate of simple interest as R%.
We know that, amount of simple interest is given as A = P + SI where P is the principal amount and SI is the simple interest. Hence, we get:
\[\begin{align}
  & \Rightarrow 35246=200000+SI \\
 & \Rightarrow SI=Rs.\left( 35246-20000 \right) \\
 & \Rightarrow SI=Rs.15246 \\
\end{align}\]
So simple interest is Rs.15,246.
Now, let us use SI, P, and T to find R using the formula of SI given by $SI=\dfrac{P\times R\times T}{100}$.
Putting values of SI, P and T we get:
\[\begin{align}
  & \Rightarrow 15246=\dfrac{20000\times R\times 5}{100} \\
 & \Rightarrow 15246=\dfrac{100000\times R}{100} \\
 & \Rightarrow 15246=1000\times R \\
 & \Rightarrow R=\dfrac{15246}{1000} \\
 & \Rightarrow R=15.246\% \\
\end{align}\]
Hence, rate of simple interest is 15.246% per annum.

Note: In this question, we had to find the rate of interest per annum. Since the rate of interest is calculated in percentage, students can make the mistake of dividing the found rate of interest by 100 to get a percentage. But they should know that we had already divided the rate by 100 in the formula of simple interest. While using the formula, make sure that the time period is in years only. Don't forget to put the percentage sign after finding the answer.