Question

Find the C.I on Rs. 5,000 at 10% per annum compounded semi-annually for \[\dfrac{11}{2}\] years.

Answer 1

Hint:For the given question, we will use the formula of compound interest, i.e. CI is given by:
\[CI=A-P\]
Where \[A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}\]
Here, ‘P’ is principal, ‘r’ is rate, ‘n’ is number of compounds per year and ‘t’ is time in years.

Complete step-by-step answer:
We have been asked to find the compound interest of Rs. 5,000 at 10% per annum compounded semi annually for \[\dfrac{11}{2}\] years.
We know the compound interest formula is:
\[CI=A-P\]
Where \[A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}\]
Here, ‘P’ is principal, ‘r’ is rate, ‘n’ is number of compounds per year and ‘t’ is time in years.
So we have P=5000, r=10%=0.1, n=2 and t= \[\dfrac{11}{2}\] years.
\[\begin{align}
  & \Rightarrow A=5000{{\left( 1+\dfrac{0.1}{2} \right)}^{2\times \dfrac{11}{2}}} \\
 & \Rightarrow A=5000{{\left( 1+0.05 \right)}^{11}} \\
 & \Rightarrow A=5000{{\left( 1.05 \right)}^{11}} \\
 & \Rightarrow A=5000\times 1.71 \\
\end{align}\]
\[\Rightarrow A=Rs.8550\]
Compound interest (CI) = Amount (A) – Principal (P)
CI = 8550 – 5000
CI = Rs. 3550
Therefore, the compound interest for the given principal, rate and time is equal to Rs. 3550.

Note: Be careful while doing calculation and use the formula very carefully. Also, we can use the binomial theorem to find the eleventh power of the number during calculation to find the value of compound interest (CI). Also, remember that the interest is compounded semi-annually means that the compounded period is six months.