Question

Find the CI on Rs. 7000 at 10% p.a compounded annually for 4 years.

Answer 1

Hint: From the question, it is given that the initial amount is equal to Rs. 7000, the interest for the initial amount is equal to 10% and the time for which the annual interest is calculated is equal to 4 years. We know that if P is the initial amount, r is the interest per year and A is the total amount obtained after t years, then \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\]. Now from the question, we should write the value of A, P, r and t. By using this formula, we should find the value of A. If A is the compound amount after t years, P is the initial amount and C.I is the compound interest for 4 years, then \[C.I=A-P\]. So, by the values of A and P, we should find the values of C.I.


Complete step-by-step answer:
Before solving the question, we should know that if P is the initial amount, r% is the interest per year and A is the total amount obtained after t years, then \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\].

From the question, it is given that the initial amount is equal to Rs. 7000, the interest for the initial amount is equal to 10% and the time for which the annual interest is calculated is equal to 4 years.
We know that if P is the initial amount, r is the interest per year and A is the total amount obtained after t years, then \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\].
So, it is clear that
\[\begin{align}
  & P=7000....(1) \\
 & r=10........(2) \\
 & t=4........(3) \\
\end{align}\]
Now from the values of P, r and t, we have to find the value of A.
\[\begin{align}
  & \Rightarrow A=\left( 7000 \right){{\left( 1+\dfrac{10}{100} \right)}^{4}} \\
 & \Rightarrow A=\left( 7000 \right){{\left( 1+\dfrac{1}{10} \right)}^{4}} \\
 & \Rightarrow A=\left( 7000 \right){{\left( \dfrac{11}{10} \right)}^{4}} \\
 & \Rightarrow A=\left( 7000 \right)\left( \dfrac{14641}{10000} \right) \\
 & \Rightarrow A=\left( 7 \right)\left( \dfrac{14641}{10} \right) \\
 & \Rightarrow A=10,248.7.....(4) \\
\end{align}\]
If A is the compound amount after t years, P is the initial amount and C.I is the compound interest for 4 years, then
\[C.I=A-P.....(5)\]
Now let us substitute equation (1) and equation (4) in equation (5), then we get
\[\begin{align}
  & \Rightarrow C.I=10,248.7-7000 \\
 & \Rightarrow C.I=3,248.7.....(6) \\
\end{align}\]
So, from equation (6) we can say that the value of C.I is equal to Rs.3,248.7.

Note: Some students have a misconception that if P is the initial amount, r is the interest per year and A is the total amount obtained after t years, then \[A=P{{\left( 1+r \right)}^{t}}\]. If this formula is applied, then the value of A is obtained as follows.
\[\begin{align}
  & \Rightarrow A=\left( 7000 \right){{\left( 1+10 \right)}^{4}} \\
 & \Rightarrow A=\left( 7000 \right){{\left( 11 \right)}^{4}} \\
 & \Rightarrow A=\left( 7000 \right)\left( 14641 \right) \\
 & \Rightarrow A=\left( 7 \right)\left( \dfrac{14641}{10} \right) \\
 & \Rightarrow A=1,024,87000.....(1) \\
\end{align}\]
Now from equation (1), it is clear that the value of A is equal to 1,024,87000. But we know that the value of A is equal to Rs.10,248.7.
So, this misconception should get avoided.