A person invested ₹ $10,000$ in $8 \%$, ₹ $25$ shares at ₹ $40$. After a year, the shares were sold at ₹ $42$ each and the proceeds (including the dividend) were invested in $9 \%$, $\;$ ₹ $10$ shares at ₹ $11$. Find:
- the dividend for the first year;
- the new number of shares bought;
- the percentage increase in the return on the original investment.
Investment $= $ ₹ $10,000$
Dividend $\% = 8 \%$
Nominal Value (N.V) of each share $= $ ₹ $25$
Market Value (M.V) of each share $= $ ₹ $40$
- Number of shares bought $= \dfrac{\text{Investment}}{\text{M.V of each share}} = \dfrac{10,000}{40} = 250$
Dividend on $1$ share $= 8 \% $ of ₹ $25 = \dfrac{8}{100} \times 25 = $ ₹ $2$
$\therefore \;$ Dividend for first year $= $ ₹ $\left(2 \times 250\right) = $ ₹ $500$ - Since each share is sold for ₹ $42$,
$\therefore \;$ Proceeds (including dividend) $= 250 \times 42 + 500 = $ ₹ $11,000$
$\therefore \;$ Sum invested $= $ proceeds $= $ ₹ $11,000$
Nominal value (N.V) of each new share $= $ ₹ $10$
Market value (M.V) of each new share $= $ ₹ $11$
$\therefore \;$ Number of new shares bought $= \dfrac{\text{Investment}}{\text{M.V of each share}} = \dfrac{11,000}{11} = 1000$ - New dividend $= 9 \%$
Dividend on $1$ share $= 9 \% $ of ₹ $10 = \dfrac{9}{100} \times 10 = $ ₹ $0.90$
$\therefore \;$ Annual dividend (income) in the second year $= $ ₹ $\left(0.90 \times 1000\right) = $ ₹ $900$
$\therefore \;$ Increase in return $= $ ₹ $\left(900 - 500\right) = $ ₹ $400$
$\therefore \;$ $\%$ Increase in return (on the original investment)
$= \dfrac{\text{Increase}}{\text{Original investment}} \times 100 \% = \dfrac{400}{10,000} \times 100 = 4 \%$