Question

A man holds 56 shares of a bank and receive a dividend of Rs. 31.50 per quarter. If the dividend he receives be 9% per annum, find the face value of a share.

Answer 1

Step 1:

Given information:

Number of shares$=56$

Quarter dividend$=\mathrm{Rs}.31.50$

Rate of dividend$=9\%\mathrm{per}\mathrm{annum}$

Step 2:

Calculate face value of share:

Let face value of one share is $\mathrm{Rs}.x$

So, face value of 56 shares$=56\times x=\mathrm{Rs}.56x$

It is given that the quarterly dividend is Rs.31.50.

$\begin{array}{rcl}\therefore \mathrm{Annual}\mathrm{dividend}& =& 4\times 31.50\\ & =& \mathrm{Rs}.126\end{array}$

The man receives an annual dividend of Rs.126 with rate of 9% per annum.

$$\begin{gathered} \mathrm{Total}\mathrm{dividend}=\mathrm{Rate}\mathrm{of}\mathrm{dividend}\times \mathrm{Face}\mathrm{value}\mathrm{of}56\mathrm{shares} \\ \Rightarrow 126=9\%\times 56x \\ \Rightarrow 126=56x\times \frac{9}{100} \\ \Rightarrow x=\frac{126\times 100}{56\times 9} \\ \therefore x=\mathrm{Rs}.25 \end{gathered}$$

Hence, the face value of one share is Rs.25.