Question

Salman invests a sum of money in $₹50$ shares, paying $15\%$ dividend quoted at $20\%$ premium. If his annual dividend is $₹600$, then calculate
(i) the number of shares, he bought.
(ii) his total investment.
(iii) the rate of return on his investment.

Answer 1

Step 1: Given data

Annual Dividend value$=₹600$

Face value$=₹50$

Rate of dividend$=15\%$

Premium%$=20\%$

Step 2: Calculate the number of shares bought by Salman

$$\begin{gathered} \mathbf{\left(}\mathit{i}\mathbf{\right)}\mathbf{}\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathbf{}\mathit{D}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}=\mathbf{}\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}\mathbf{\times }\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{\times }\frac{\mathit{R}\mathit{a}\mathit{t}\mathit{e}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}}{\mathit{100}} \\ \therefore \mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}=\mathit{}\frac{\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathit{}\mathit{D}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}\mathit{\times }\mathit{100}}{\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathit{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathit{\times }\mathit{R}\mathit{a}\mathit{t}\mathit{e}\mathit{}\mathit{o}\mathit{f}\mathit{}\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}\mathit{\%}} \end{gathered}$$

$$\begin{gathered} =\frac{600\times 100}{15\times 50} \\ =80\mathrm{shares} \end{gathered}$$

Step 3: Calculate the investment done by Salman

(ii) $\mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}=\mathbf{}\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{+}\mathit{P}\mathit{r}\mathit{e}\mathit{m}\mathit{i}\mathit{u}\mathit{m}\mathbf{\%}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{F}\mathit{a}\mathit{c}\mathit{e}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}$

$=50+\frac{20}{100}\times 50=50+10=₹60$

and, $\mathit{I}\mathit{n}\mathit{v}\mathit{e}\mathit{s}\mathit{t}\mathit{m}\mathit{e}\mathit{n}\mathit{t}=\mathit{M}\mathit{a}\mathit{r}\mathit{k}\mathit{e}\mathit{t}\mathit{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e}\mathbf{\times }\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{h}\mathit{a}\mathit{r}\mathit{e}\mathit{s}$

$=60\times 80=₹4800$

Step 4: Find the return% on his investment

(iii) $\mathit{R}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathbf{\%}=\mathbf{}\frac{\mathit{A}\mathit{n}\mathit{n}\mathit{u}\mathit{a}\mathit{l}\mathit{}\mathit{D}\mathit{i}\mathit{v}\mathit{i}\mathit{d}\mathit{e}\mathit{n}\mathit{d}}{\mathit{I}\mathit{n}\mathit{v}\mathit{e}\mathit{s}\mathit{t}\mathit{m}\mathit{e}\mathit{n}\mathit{t}}\mathit{\times }\mathit{100}$

$$\begin{gathered} =\frac{600}{4800}\times 100 \\ =12.5\% \end{gathered}$$

Hence,

(i) Number of shares Salman bought is $\mathbf{80}$.

(ii) Salman's total investment is $\mathbf{₹}\mathbf{4800}$.

(iii) Salman's rate of return on his investment is $\mathbf{12}\mathbf{.}\mathbf{5}\mathbf{\%}$.