A person buys $500$, ₹ $20$ shares at a discount of $20\%$ and receives a return of $10\%$ on her money. Calculate the amount invested and the rate of dividend paid by the company.
Number of shares $= 500$
Nominal value of each share $= N.V = $ ₹ $20$
Market value of each share $= M.V = $ ₹ $20 - 20 \%$ of ₹ $20 = $ ₹ $20 \; - $ ₹ $4 = $ ₹ $16$
Rate of return $= 10\%$
Amount invested $=$ Number of shares $\times$ M.V of 1 share
i.e. $\;$ Amount invested $= 500 \times $ ₹ $16 = $ ₹ $8000$
Now, $\;$ $\text{Rate of return} \times M.V = \text{Rate of dividend} \times N.V$
$\therefore \;$ $\text{Rate of dividend} = \dfrac{\text{Rate of return} \times M.V}{N.V}$
i.e. $\;$ $\text{Rate of dividend} = \dfrac{10}{100} \times 16 \times \dfrac{1}{20} = \dfrac{8}{100} = 8\%$