Question 1: A man invests Rs. 8,800 in buying shares of a company of face value of Rs. 100 each at a premium of 10%. If he ears Rs. 1,200 at the end of the year as dividend. Find; i) The number of shares he has in the company. ii) The dividend percent per share. [2001]

$\displaystyle \text{Nominal price of the share } = 100 \text{ Rs. }$

$\displaystyle \text{Cost price of the share } = 100 +10 = 110 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{8800}{110} = 80$

$\displaystyle \text{Dividend earned } = 1200 \text{ Rs. }$

$\displaystyle \text{Let the dividend } \% = x$ Therefore

$\displaystyle 80 \times 100 \times \frac{x}{100} = 1200 \Rightarrow x = 15\%$

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Question 2: A man invests Rs. 1680 in buying shares of nominal value Rs. 24 and selling at 12% premium. The dividend on the shares is 15% per annum. Calculate: i) The number of shares he buys; ii) The dividend he receives. [1999]

$\displaystyle \text{Nominal price of the share } 24 \text{ Rs. }$

$\displaystyle \text{Selling price of the share } = 24 +24 \times \frac{12}{100} = 26.88 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{1680}{26.88} = 62.5$

$\displaystyle \text{Dividend received } = 62.5 \times 24 \times \frac{15}{100} = 225 \text{ Rs. }$

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Question 3: By investing Rs. 7500 in a company paying 10% dividend, an annual income of Rs. 500 is received. What price is paid for each of Rs.100 shares? [1990]

Let the premium $\displaystyle = x \text{ Rs. }$

Market price $\displaystyle = (100+x) \text{ Rs. }$

Therefore

$\displaystyle \frac{7500}{(100+x)} \times 100 \times {10}{100} = 500$

$\displaystyle 750 = 500+5x$

$\displaystyle x = 50$

Hence the price paid for each share $\displaystyle = 100+50 = 150 \text{ Rs. }$

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Question 4: A man invests Rs. 20,020 in buying shares of N.V. Rs. 26 at 10% premium. The dividend on the shares is 15% per annum. Calculate: i) The number of shares he buys; ii) The dividend he receives annually; iii) The rate of interest he gets on his money. [2012]

$\displaystyle \text{Number of shares } = \frac{20020}{26+2.6} = 700$

$\displaystyle \text{Dividend } = 700 \times 26 \times \frac{15}{100} = 2730 \text{ Rs. }$

$\displaystyle \% \text{ rate of interest he gets} = \frac{2730}{20020} \times 100 = 13.64\%$

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Question 5: A man invested Rs. 45,000 in 15% Rs.100 shares quoted at Rs. 125, when the M.V. of these shares rose to Rs. 140, he sold some shares, just enough to raise Rs. 8400. calculate: i) The number of shares he still holds; ii) The dividend due to him on these remaining shares. [2004]

$\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 125 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{45000}{125} = 360$

Selling Value of the share $\displaystyle = 140 \text{ Rs. }$

Amount of money raised $\displaystyle = 8400 \text{ Rs. }$

Therefore number of shares sold $\displaystyle = \frac{8400}{140} = 60$

Shares left $\displaystyle = 360 - 60 = 300$

$\displaystyle \text{Dividend earned on remaining shares } = 300 \times 100 \times \frac{15}{100} = 4500 \text{ Rs. }$

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Question 6: Vivek invests Rs. 4,500 in 8%, Rs.10 shares at Rs. 15. He sells the shares when the price rises to Rs. 30, and invests the proceeds in 12% Rs. 100 shares at Rs. 125. Calculate; i) The sale proceeds ii) The number of Rs. 125 shares he buys; iii) The change in his annual income from dividend. [2010]

First Investment

Let the amount invested $\displaystyle = 4500 \text{ Rs. }$

$\displaystyle \text{Nominal Value of the share } = 10 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 15 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 8\%$

$\displaystyle \text{Number of shares bought } = \frac{4500}{15} = 300$

Sale Proceed $\displaystyle = 300 \times 30 = 9000 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 300 \times 10 \times \frac{8}{100} = 240 \text{ Rs. }$

Second Investment

Therefore the amount invested $\displaystyle = 9000 \text{ Rs. }$

$\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 125 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 12\%$

$\displaystyle \text{Number of shares bought } = \frac{9000}{125} = 72$

$\displaystyle \text{Dividend earned } = 72 \times 100 \times \frac{12}{100} = 864 \text{ Rs. }$

Hence the change in income $\displaystyle = 864-240 = 624 \text{ Rs. }$

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Question 7: Mr. Parekh invested Rs. 52,000 on Rs. 100 shares at a discount of Rs. 20 paying 8% dividend. At the end of one year he sells the shares at a premium of Rs. 20; find: i) The annual dividend; ii) The profit earned including his dividend. [2011]

$\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 80 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{52000}{80} = 650$

$\displaystyle \text{Dividend earned } = 650 \times 100 \times \frac{8}{100} = 5200 \text{ Rs. }$

$\displaystyle \text{Sale proceeds } = 650 \times 120 = 78000 \text{ Rs. }$

$\displaystyle \text{Profit } = (78000-52000)+5200 = 31200 \text{ Rs. }$

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Question 8: Salman buys 50 shares of face value Rs. 100 available at Rs. 132. i) What is his investment? ii) If the dividend is 7.5%, what will be his annual income? iii) If he wants to increase his annual income by Rs. 150, how many extra shares should he buy? [2013]

$\displaystyle \text{Nominal Value of the share } = 100 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 132 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = 50$

$\displaystyle \text{Investment } = 50 \times 132 = 6600 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 50 \times 100 \times \frac{7.5}{100} = 375 \text{ Rs. }$

$\displaystyle \text{ Dividend earned on 1 share } = 1 \times 100 \times \frac{7.5}{100} = 7.5 \text{ Rs. }$

$\displaystyle \text{Therefore to earn 150 Rs. more, one needs to buy } \frac{150}{7.5} = 20$ shares.

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Question 9: Salman invests a sum of money in Rs. 50 shares, paying 15% dividend quoted at 20% premium. If his annual dividend is Rs. 600, Calculate; i) The number of shares he bought; ii) His total investment; ii) The rate of return on his investment. [2004]

$\displaystyle \text{Nominal Value of the share } = 50 \text{ Rs. }$

$\displaystyle \text{Market Value of the share } = 60 \text{ Rs. }$

$\displaystyle \text{Dividend earned } = 15\%$

$\displaystyle \text{Dividend earned on 1 share }= 1 \times 50 \times \frac{15}{100} = 7.5 \text{ Rs. }$

$\displaystyle \text{Number of shares bought } = \frac{600}{7.5} = 80$

$\displaystyle \text{Investment } = 80 \times 60 = 4800 \text{ Rs. }$

$\displaystyle \% return = \frac{600}{4800} \times 100 = 12.5\%$