A person bought ₹ $\; 100$ shares of dividend $9 \%$ selling at a certain price. If the rate of return is $7.5 \%$, calculate:
- the market value of each share;
- the amount to be invested to obtain an annual income of ₹ $\; 1260$;
- how many more shares should be bought to increase the income to ₹ $\; 1890$.
Nominal value (N.V) of each share $= $ ₹ $ 100$
Rate of dividend $= 9 \%$
Rate of return $= 7.5 \%$
-
Let market value (M.V) of each share $= $ ₹ $ x$
Now, $\;$ $\text{Rate of return} \times M.V = \text{Rate of dividend} \times N.V$
i.e. $\;$ $\dfrac{7.5}{100} \times x = \dfrac{9}{100} \times 100$
$\implies$ $x = \dfrac{900}{7.5} = 120$
i.e. $\;$ Market value of each share $= $ ₹ $ 120$
-
Total annual income $= $ ₹ $ 1260$
Annual income on $1$ share $= 9 \%$ of ₹ $ 100 = $ ₹ $ 9$
$\begin{aligned} \text{Number of shares bought} & = \dfrac{\text{Total annual income}}{\text{Annual income on 1 share}} \\\\ & = \dfrac{1260}{9} \\\\ & = 140 \end{aligned}$
$\therefore \;$ Amount to be invested $=$ Number of shares bought $\times$ M.V of 1 share
i.e. $\;$ Amount to be invested $= 140 \times $ ₹ $ 120 = $ ₹ $ 16,800$
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New annual income $= $ ₹ $ 1890$
$\begin{aligned} \therefore \; \text{Number of shares} & = \dfrac{\text{Total annual income}}{\text{Annual income on 1 share}} \\\\ & = \dfrac{1890}{9} \\\\ & = 210 \end{aligned}$
$\therefore \;$ Number of extra shares $= 210 - 140 = 70$