Question

Find compound interest paid when a sum of Rs.10000 is invested for 1 year and 3 months at \[8\dfrac{1}{2}%\] per annum, compounded annually.

Answer 1

Hint: Proceeding for this type of question we always go for applying the formula of compound interest which is given in the relation of the principal P, the rate of interest r and the number of years n and then we substitute the value of all and calculate accordingly to get the result.

Complete step by step answer:
Given principal amount Rs.10000 invested for 1 year and 3 months at \[8\dfrac{1}{2}%\] per annum. We have to find out the compound interest of the amount.
First of all, we find the compound interest for 1 year, then n=1 year.
Formula of compound interest,
  \[A=P{{(1+\dfrac{r}{100})}^{n}}\]
where,
A= Amount,
P= Principal amount,
r= rate of interest applied per year,
n= number of years.
Given, Principal P= 10000rs, rate of interest r = \[8\dfrac{1}{2}%\] and the number of years n=1.
Substituting the values of Principal P, interest rate r and number of years n in the formula given below,
\[A=P{{(1+\dfrac{r}{100})}^{n}}\]

\[\begin{align}
  & \Rightarrow A=10000{{\left( 1+\dfrac{8\dfrac{1}{2}}{100} \right)}^{1}} \\
 & \Rightarrow A=10000\left( 1+\dfrac{\dfrac{17}{2}}{100} \right) \\
 & \Rightarrow A=10000\left( 1+\dfrac{17}{200} \right) \\
 & \Rightarrow A=10000\left( \dfrac{200+17}{200} \right) \\
 & \Rightarrow A=10000\left( \dfrac{217}{200} \right) \\
 & \Rightarrow A=10850 \\
\end{align}\]
Now this value of amount becomes equal to the principal for calculating compound interest of last 3 months.
Then for 3 months,
Principal P = 10850, Rate \[r=\dfrac{17}{2}%\] and time t = 3 months which is equal to \[\dfrac{1}{4}year\].
The formula of simple interest is \[SI=\dfrac{\operatorname{PrT}}{100}\].
Substituting the values of all we get,
\[\begin{align}
  & \Rightarrow SI=\dfrac{10850\left( \dfrac{17}{2} \right)\left( \dfrac{1}{4} \right)}{100} \\
 & \Rightarrow SI=\dfrac{18445}{80} \\
 & \Rightarrow SI=230.56 \\
\end{align}\]

Now interest for 1 year = Amount – P(for 1 year)
Implies Interest for 1 year = 10850-10000 = Rs. 850.
Then the Compound interest = interest for 1 year + Simple interest obtained as 230.56.
Then we get the value of compound interest as CI = Rs. 1080.56.
Therefore, the compound interest per annum on the given values of principal and rate of interest is equal to Rs. 1080.56.

Note: The important concept in this question is while calculating the amount and the interest for the next 3 months in total one year and three month we will use the amount obtained for one year as the principal and then calculate the simple interest and compound interest using the formula to obtain the answer.