Question

Calculate the amount and the compound interest on Rs.10800 for 3 years at \[\dfrac{25}{2}%\] per annum compounded annually.

Answer 1

Hint: We will solve this question and try to calculate the amount and compound interest using the formula\[A=P{{\left( 1+\dfrac{R}{100} \right)}^{N}}\], where A is the amount, P is the principal, R is the rate of interest and N is the time of investment. Substituting values of different variables we will get our required result.

Complete step-by-step answer:

We are given with Principal P= Rs.10800, Rate of interest R= \[\dfrac{25}{2}%\] and the time of investment as N=3 years.
We have the formula to calculate amount as \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{N}}\], where A is the amount, P is the principal, R is the rate of interest and N is the time of investment. Now we will solve the formula using the values that have been provided to us in the question.
\[A=P{{\left( 1\dfrac{R}{100} \right)}^{N}}\]
Substituting the values of Principal, rate of interest and time of investment in the above formula we have,
\[\Rightarrow A=10800{{\left( 1+\dfrac{\dfrac{25}{2}}{100} \right)}^{3}}\]
\[\begin{align}
  & \Rightarrow A=10800{{\left( 1+\dfrac{25}{200} \right)}^{3}} \\
 & \Rightarrow A=10800{{\left( 1+\dfrac{1}{8} \right)}^{3}} \\
 & \Rightarrow A=10800{{\left( \dfrac{9}{8} \right)}^{3}} \\
\end{align}\]
 Taking the cube of 9 and 8 and proceeding we have,
\[\begin{align}
  & A=10800\left( \dfrac{729}{512} \right) \\
 & \Rightarrow A=10800\left( 1.423 \right) \\
 & \Rightarrow A=15,377.34 \\
\end{align}\]

Hence, we got the final amount as Rs.15377.34
Now we will find the compound interest by using the formula, CI = A-P, where CI is the compound interest, A is the amount and P is the principal.
Substituting the values in the formula for Compound interest we have,
\[\begin{array}{*{35}{l}}
   CI=15377.34-10800 \\
   ~\Rightarrow CI=4577.34 \\
\end{array}\]
Therefore, the compound interest CI= Rs.4577.34
Hence, we got the final amount A= Rs.15377.34 and the compound interest CI= Rs.4577.34.

Note: Always remember in these types of questions if the time is not given in the form of year then always convert the time in year and then proceed to calculate the compound interest and the amount using the above stated formula.