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]

Answer:

\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]

Answer:

\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]

Answer:

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]

Answer:

\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]

Answer:

\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]

Answer:

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]

Answer:

\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. }  

\displaystyle  \\

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]

Answer:

\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]

Answer:

\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\%