Question

Find the amount from the investment of Rs.4500 for two years at 5 paise per rupee interest.

Answer 1

Hint: We know that if A is the amount obtained after T years, P is the initial amount invested and R is the rate of interest then \[A=P\left( 1+\dfrac{RT}{100} \right)\]. We know that rate of interest and interest are related as \[R=100I\]. We have been given that 5 paise per rupee interest, so this data can be interpreted as \[I=\dfrac{5}{100}\] . By using this formula, we can find the value of A. So, by using this formula, we can find the amount from the investment of Rs.4500 for two years at 5 paise per rupee interest.

Complete step by step answer:
Before solving the question, we should know that if A is the amount obtained after T years, P is the initial amount invested and R is the rate of interest then \[A=P\left( 1+\dfrac{RT}{100} \right)\].
From the question, we were given that the amount of investment of Rs.4500 for 2 years at 5 paise per rupee interest.
So, now we should find interest.
We were given that there is 5 paise per rupee interest.
Let us assume the interest is equal to I.
So, we can write
\[I=\dfrac{5}{100}.....(1)\]
Now we should find the rate of interest. We know that if the value of interest is equal to I, then R is the rate of interest if \[R=100I\].
So, from equation (1), we can write
\[\begin{align}
  & \Rightarrow R=100\left( \dfrac{5}{100} \right) \\
 & \Rightarrow R=5....(2) \\
\end{align}\]
Let us assume the initial interest is equal to P.
Then we get
\[\Rightarrow P=4500.....(3)\]
Let us assume the time period is equal to T.
Then we get
\[\Rightarrow T=2.....(4)\]
We know that if A is amount obtained after T years, P is initial amount invested and R is rate of interest then \[A=P\left( 1+\dfrac{RT}{100} \right)\].
Now from equation (2), equation (3) and equation (4), we should calculate the value of A.
\[\begin{align}
  & \Rightarrow A=4500\left( 1+\dfrac{\left( 5 \right)\left( 2 \right)}{100} \right) \\
 & \Rightarrow A=4500\left( 1+\dfrac{10}{100} \right) \\
 & \Rightarrow A=4500\left( 1+\dfrac{1}{10} \right) \\
 & \Rightarrow A=4500\left( \dfrac{11}{10} \right) \\
 & \Rightarrow A=4500\left( \dfrac{11}{10} \right) \\
 & \Rightarrow A=450\left( 11 \right) \\
 & \Rightarrow A=4950.....(5) \\
\end{align}\]
From the equation, the value of A is equal to 4950.
So, we can write that the amount from the investment of Rs.4500 for two years at 5 paise per rupee interest is equal to Rs.4500.

Note:
Students may have a misconception that \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{t}}\]. If this misconception is followed, then the value of A is obtained as follows:
\[\begin{align}
  & \Rightarrow A=4500{{\left( 1+\dfrac{\left( 5 \right)}{100} \right)}^{2}} \\
 & \Rightarrow A=4500{{\left( \dfrac{105}{100} \right)}^{2}} \\
 & \Rightarrow A=4500{{\left( \dfrac{26}{25} \right)}^{2}} \\
 & \Rightarrow A=4500\left( \dfrac{576}{525} \right) \\
 & \Rightarrow A=4937.14 \\
\end{align}\]
So, it is clear that the amount from the investment of Rs.4500 for two years at 5 paise per rupee interest is equal to 4937.14. But we know that the amount from the investment of Rs.4500 for two years at 5 paise per rupee interest is equal to Rs.4500. So, this misconception should be avoided.