Question

Find the compound interest on 2500 for 6 months at $ 8\% $ per annum, when compounded quarterly.

Answer 1

Hint: Type of question is purely based on the calculation of compound interest. Which states that $ A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}} $ in which ‘A’ is the Total amount, ’P’ is the principal amount, r is the rate of interest in the ratio form, n is the interest compounded in a year and t is the time period of interest in year. Now from here we will get the total amount after adding principal amount to interest, so for compound interest we have to subtract the total amount i.e. ‘A’ from the principal amount i.e. ‘P’.

Complete step by step answer:
So moving ahead with our question, we have;
Principal amount $ =2500Rs. $
Rate of interest $ =8\% $
In ratio form rate $ =\dfrac{8}{100} $
Rate compounded in a year i.e. ‘n’ $ =4 $
Time period $ =6 $ months
In year $ =\dfrac{6}{12}=\dfrac{1}{2} $ years
Now put the value in the formula and solve to find out the total amount. So we will get;
 $ \begin{align}
  & A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}} \\
 & A=2500{{\left( 1+\left( \dfrac{8}{100} \right)\dfrac{1}{4} \right)}^{\left( 4 \right)\left( \dfrac{1}{2} \right)}} \\
 & A=2500{{\left( 1+\dfrac{2}{100} \right)}^{2}} \\
 & A=2500{{\left( \dfrac{102}{100} \right)}^{2}} \\
 & A=2601 \\
\end{align} $
So, total amount is $ 2601Rs. $
For compound interest we had to subtract the total amount by principal amount. So we will get compound interest i.e.
Total amount $ - $ Principal amount $ = $ compound interest
 $ \begin{align}
  & A-P=compound\text{ }interest \\
 & 2601-2500=compound\text{ }interest \\
 & compound\text{ }interest=101Rs. \\
\end{align} $
Hence the answer is $ 101Rs $ , i.e. compound interest is $ 101Rs $ .

Note: Keep remember that we had formula $ A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}} $ is for total amount after calculation the compound interest on an amount. It is not a formula for calculating compound interest.