Question

A man invests $₹8800$ in a company paying $6\%$ dividend when a share of face value $₹100$ is selling at $₹60$ premium. What is the percentage return on his investment?

Answer 1

Step 1: Given data

Total investment$=₹8800$

Rate of dividend$=6\%$

Premium value$=₹60$

Face value$=₹100$

Step 2: Calculate the market value of the share

$$\begin{gathered} \mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}=\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{}\mathbf{+}\mathbf{}\mathit{P}\mathit{r}\mathit{e}\mathit{m}\mathit{i}\mathit{u}\mathit{m} \\ =100+60 \\ =₹160 \end{gathered}$$

Step 3: Find the number of shares bought by the man

$$\begin{gathered} \mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}=\frac{\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathit{}\mathit{i}\mathit{n}\mathit{v}\mathit{e}\mathit{s}\mathit{t}\mathit{m}\mathit{e}\mathit{n}\mathit{t}}{\mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathit{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}} \\ =\frac{8800}{160} \\ =55\mathrm{shares} \end{gathered}$$

Step 4: Find the total annual income of the man earned at a 6% rate of dividend

$$\begin{gathered} \mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathit{}\mathit{i}\mathit{n}\mathit{c}\mathit{o}\mathit{m}\mathit{e}=\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathit{\times }\frac{\mathit{R}\mathit{a}\mathit{t}\mathit{e}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}}{\mathit{100}}\mathit{\times }\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathit{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e} \\ =55\times \frac{6}{100}\times 100 \\ =₹330 \end{gathered}$$

Step 5: Find the rate of return on investment

$$\begin{gathered} \mathit{R}\mathit{a}\mathit{t}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{r}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}=\frac{\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathit{}\mathit{I}\mathit{n}\mathit{c}\mathit{o}\mathit{m}\mathit{e}}{\mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathit{}\mathit{i}\mathit{n}\mathit{v}\mathit{e}\mathit{s}\mathit{t}\mathit{m}\mathit{e}\mathit{n}\mathit{t}}\mathbf{\times }\mathbf{100} \\ =\frac{330}{8800}\times 100 \\ =3.75\% \end{gathered}$$

Final Answer: The percentage return on the man's total investment is $\mathbf{3}\mathbf{.}\mathbf{75}\mathbf{\%}$.