Question

By using the formula, find the amount and compound interest on $\text{Rs}\text{. 6000}$ for $2$ years at $9\%$ per annum compounded annually?

Answer 1

Hint: When we calculate the interest in the Compounded method it gives the total amount to be paid after a particular time period. The formula we generally use to calculate the total amount in compounded method is
$A=P{{\left( 1+\dfrac{R}{n} \right)}^{nt}}$
Where
              $A$ is the Total amount.
     $P$ is the principal amount.
     $R$ is the interest rate in Decimals.
     $n$ is the number of times that the interest is compounded yearly.
     $t$ is the time period in years.
If you want to calculate the interest in compounded method use the below formula
Interest $=$ Total Amount$\left( A \right)$$-$Principle Amount$\left( P \right)$.
So, using the above formulas we will calculate the total amount and interest in the compounded method.

Complete step by step answer:
Given that,
Principal amount is $P=6000$
Rate of Interest is $R=9\%=\dfrac{9}{100}=0.09$
Time period is $t=2$
The interest is compounded annually, then
$n=1$
Now the total amount is given by
$\begin{align}
  & A=P{{\left( 1+\dfrac{R}{n} \right)}^{nt}} \\
 & \Rightarrow A=6000{{\left( 1+\dfrac{0.09}{1} \right)}^{1\left( 2 \right)}} \\
 & \Rightarrow A=6000{{\left( 1+0.09 \right)}^{2}} \\
 & \Rightarrow A=6000{{\left( 1.09 \right)}^{2}} \\
 & \Rightarrow A=7128.6 \\
\end{align}$
Hence the total amount to be paid after $2$years is Rs.$7128.6$
Now the compounded interest is
$\begin{align}
  & \text{Interest }=A-P \\
 & \Rightarrow \text{Interest }=7128.6-6000 \\
 & \Rightarrow \text{Interest }=1128.6 \\
\end{align}$

Hence the compounded interest is Rs.$1128.6$.

Note: Please understand the difference between the simple interest and compound interest. Where simple interest gives the total interest to be paid after the given time period using the formula
$\text{SI}=\dfrac{PRT}{100}$
Where
     $P$ is the principal amount.
     $R$ is the rate of interest in percentage.
     $T$ is the time period in years.
From above formula we will get the Simple Interest to be paid for the time period $T$. If you want to calculate the total amount to be paid, we have to add this simple interest to principal amount to get the total amount. Now we will be calculating the total amount for the same problem with simple interest formula
$\begin{align}
  & SI=\dfrac{6000\times 9\times 2}{100} \\
 & =1080
\end{align}$
And the total amount is given by
$\begin{align}
  & A=P+SI \\
 & \Rightarrow A=6000+1080 \\
 & \Rightarrow A=7080 \\
\end{align}$
Hence the total amount to be paid is Rs.$7080$, if the interest is simple interest.