Question

At what percent per annum will \[Rs.6300\] yield an interest of \[Rs.2100\] in \[4\] years?

Answer 1

Hint: Simple interest is the amount which we have to pay in addition to the principal amount when we take a loan from the bank. In the question, we have to find the rate at which the amount will be given. Principal amount refers to the original money that we take from the bank or any other person.

Complete step-by-step solution:
When we take a loan from the bank then the bank charges a rate of interest on the amount which we take from the bank for a certain period. The rate of interest will be given in percentage and the time will be in years. When you return that money to the bank then you have to pay the total amount with simple interest. Simple interest remains the same throughout but the compound interest goes on increasing. It is easy to calculate simple interest but calculating compound interest will be difficult.
There are various kinds of loans that we take from the bank and those are education loans, home loans, car loans, etc.
When you are investing something then compound interest will be beneficial but when you are borrowing something then simple interest will be beneficial because compound interest yields more money as compared to simple interest.
In the above question, it is given that the simple interest on an amount of \[Rs.6300\] is \[Rs.2100\] and the time is \[4\] years. So here we have to find the rate at which the amount is given. The rate of interest will always be placed in the form of a fraction in the question.
As we know that, the formula for simple interest is given as shown below.
\[S.I=\dfrac{P\times R\times T}{100}\]……..eq(1)
Where S.I is the simple interest, P represents the principal amount and T is the time. So we have to find the value of R, which is the rate of interest.
In the question, it is given that
\[S.I=Rs.2100\]
\[P=Rs.6300\]
\[T=4years\]
On putting these values in eq(1), the following results will be obtained.
\[\begin{align}
  & S.I=\dfrac{P\times R\times T}{100} \\
 & \Rightarrow 2100=\dfrac{6300\times R\times 4}{100} \\
\end{align}\]
\[\Rightarrow R=\dfrac{2100\times 100}{6300\times 4}\]
\[\Rightarrow R=\dfrac{100}{12}\]
\[\Rightarrow R=8.34\%\]
So the rate will be \[8.34\%\] per annum.

Note: There is another type of interest which is known as compound interest. Simple interest is based on the principal amount that we take as a loan but compound interest depends on the principal and the interest which increases in a certain period. So simple interest will be more beneficial when you are taking a loan.