Question

A sum of Rs 1000 is lent for 1 year at the rate of $7\%$ p.a. Find the interest and the amount?

Answer 1

Hint: In the above question, principal is given as Rs 1000, rate of interest is given as $7\%$ p.a. and time on which interest has been applied is 1 year. To find the interest we are going to use the formula for simple interest (S.I.) which is given as $S.I.=\dfrac{P\times R\times T}{100}$ where “P” represents principal, “R” represents rate of interest and “T” represents time and amount is calculated by adding principal with simple interest.

Complete step-by-step answer:
It is given that principal is equal to Rs 1000, rate of interest is given as $7\%$ p.a. and time on which interest has been applied is 1 year.
We are asked to find the simple interest which we will find by using the formula of simple interest.
The formula of simple interest is equal to:
$S.I.=\dfrac{P\times R\times T}{100}$………………………………...… Eq. (1)
In the above equation, “P” stands for principal, “R” stands for rate of interest and “T” represents the time period in years.
Substituting “P” as Rs 1000, “R” as $7\%$ and “T” as 1 year in eq. (1) we get,
$S.I.=\dfrac{\left( 1000 \right)\times \left( 7 \right)\times \left( 1 \right)}{100}$
In the above equation, 100 will be cancelled out from the numerator and denominator of the right hand side of the above equation.
$\begin{align}
  & S.I.=\dfrac{\left( 10 \right)\times \left( 7 \right)\times \left( 1 \right)}{1} \\
 & \Rightarrow S.I.=70 \\
\end{align}$
From the above, we have got the value of interest as Rs 70.
Now, to find the amount we are going to add the interest that we have calculated above to the principal.
$\begin{align}
  & \text{Amount}=\text{Rs}\left( 70+1000 \right) \\
 & \Rightarrow \text{Amount}=\text{Rs}1070 \\
\end{align}$
Hence, we have calculated the value of the amount as Rs 1070 and simple interest as Rs 70.

Note: Here you are lucky that time is given in years but in some problems time is not given in years. For instance in some problems time is given 1 year and 6 months then you have to first convert the time into years which will be 1.5 years then substitute in the formula of simple interest because in the formula of simple interest time should be in years.