Question

A company with \[4000\] shares of nominal value of Rs. \[110\] each declares an annual \[15\% .\] Calculate (i) the total amount of dividend paid by the company (ii) the annual income of Rajeev who holds \[88\] shares in the company. (iii) if he received only \[10\% \] on his investment, find the price Rajeev paid for each share.

Answer 1

Hint: We will start this question with solving the first part where we are asked to find the total dividend paid by the company. Then in the next two parts we are asked about Rajeev who holds some shares in the company.

Complete step-by-step answer:
We have been given that there is a company which holds \[4000\] shares of nominal value of Rs. \[110\] each declares an annual \[15\% .\]
(i) We need to find the total amount of dividend paid by the company.
We know that, total dividend $ = \dfrac{{rate}}{{100}} \times nominal{\text{ }}value \times number{\text{ of }}shares $
So, using the above formula, the total amount of dividend paid by the company $ = \dfrac{{15}}{{100}} \times 110 \times 4000 $ $ $
 $ \begin{gathered}
   = 15 \times 110 \times 40 \\
   = 66000 \\
\end{gathered} $
Thus, the total amount of dividend paid by the company is Rs. \[66000.\]
(ii) Now, we need to find the annual income of Rajeev who holds \[88\] shares in the company.
We know that, annual income $ = \dfrac{{rate}}{{100}} \times nominal{\text{ }}value \times number{\text{ of }}shares $
So, using the above formula, the annual income of Rajeev who holds \[88\] shares in the company $ = \dfrac{{15}}{{100}} \times 110 \times 88 $
 $ \begin{gathered}
   = \dfrac{{15 \times 968}}{{10}} \\
   = 1452 \\
\end{gathered} $
Thus, the annual income of Rajeev is Rs.\[\;1452.\]

(iii) Now, we need to find if Rajeev received only \[10\% \] on his investment, then how much price Rajeev paid for each share.
So, the rate of return Rajeev received on his investment \[ = {\text{ }}10\% \]
At first, we need to find the investment done by Rajeev for that we use the formula mentioned below.
Investment done $ = \dfrac{{{\text{Annual income}}}}{{Rate}} \times 100 $
Now, after putting the values in the above formula, we get
 $ \begin{gathered}
   = \dfrac{{1452 \times 100}}{{10}} \\
    \\
\end{gathered} $
\[ = {\text{ }}14520\]
Next, we need to find the market value of each share also, for that we use the formula mentioned below.
Market value $ = \dfrac{{{\text{Investment done}}}}{{{\text{total share}}}} $
Now, after putting the values in the above formula, we get
 $ = \dfrac{{14520}}{{88}} $
\[ = \]\[165\]
Thus, if Rajeev received only \[10\% \] on his investment, then the price Rajeev paid for each share is Rs.\[\;165.\]

Note: The question contains three parts, students should carefully do each part one by one and then move further, as all the parts are somewhat connected to each other. Using the formulae appropriately holds the key.