Question 1: A man buys 75, Rs. 100 shares paying 9% dividend. He buys shares at such a price that he gets 12% of his money. At what price did he buy the shares?

Answer:

Nominal Price of the share = 100 \ Rs.

Let the Market Price of the share = (100+x) \ Rs.

Dividend earned = 75 \times 100 \times \frac{9}{100} = 675 \ Rs.

Therefore

 \frac{12}{100} \times 75 \times (100+x) = 675

 9(100+x) = 675

 \Rightarrow x = -25

Therefore the market price of the share = 100-25 = 75 \ Rs.

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Question 2: By purchasing Rs. 25 gas shares for Rs. 40 each, a man gets 4 percent profit on his investment. What rate per cent is the company paying? What is his dividend if he buys 60 shares?

Answer:

Nominal Price of the share = 25 \ Rs.

Market Price of the share = 40 \ Rs.

Number of Shares bought = 60

Let the % dividend = x \ %

Therefore

 60 \times 25 \times \frac{x}{100} = 60 \times 40 \times \frac{4}{100}

 \Rightarrow 25x = 160 \ or \  x = 6.4\%

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Question 3: 100 Rs. shares of a company are available in the market at a premium of Rs. 20. Find the rate of dividend given by the company, when a man’s return on his investment is 15%.

Answer:

Nominal Price of the share = 100 \ Rs.

Market Price of the share = 120 \ Rs.

Let the % dividend = x \ %

Let us say that the person bought 100 shares.

Therefore

 100 \times 100 \times \frac{x}{100} = 100 \times 120 \times \frac{15}{100}

 \Rightarrow 100x = 120 \times 15 \ or \  x = 18\%

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Question 4: 50 shares of a company are quoted at a discount of 10%. Find the rate of dividend given by the company, the return on the investment on these shares being 20%.

Answer:

Let Nominal Price of the share = x \ Rs.

Therefore Market Price of the share = 0.9x \ Rs.

Number of Shares bought = 50

Let the % dividend = y \ %

Therefore

50 \times x \times \frac{y}{100} = 50 \times 0.9x \times \frac{20}{100}

 \Rightarrow y = 0.9 \times 20  \ or  \  y = 18\%

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Question 5: A company declares 8 per cent dividend to the shareholders. If a man receives Rs. 2840 as his dividend, find the nominal value of his shares.

Answer:

Let the nominal Value of the shares   = x \ Rs. 

Therefore x  \times \frac{8}{100} = 2840 \Rightarrow x = 35500 \ Rs. 

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Question 6: How much should a man invest in Rs. 100 shares selling at Rs. 110 to obtain an annual income of Rs. 1680, if the dividend declared is 12%?

Answer:

Nominal Price of the share = 100 \ Rs.

Market Price of the share = 110 \ Rs.

Let the number of Shares bought = x

Therefore

 x \times 100 \times \frac{12}{100} = 1680 \Rightarrow x = 140

Hence the investment = 140 \times 110 = 15400 \ Rs. 

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Question 7: A company declares a dividend of 11.2% to all its share holders. If its Rs. 60 share is available in the market at a premium of 25%, how much should a person invest, in buying the shares of this company, in order to have an annual income of Rs. 1680?

Answer:

Nominal Price of the share = 60 \ Rs.

Market Price of the share = 75 \ Rs.

Let the number of Shares bought = x

Therefore

 x \times 60 \times \frac{11.2}{100} = 1680 \Rightarrow x = 250

Hence the investment = 250 \times 75 = 18750 \ Rs. 

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Question 8: A man buys 400, 20 Rs. shares at a premium of Rs. 4 each and receives a dividend of 12%. Find: i) The amount invested by him; ii) His total income from the shares. iii) Percentage return on his money;

Answer:

Nominal Price of the share = 20 \ Rs.

Market Price of the share = 24 \ Rs.

The number of Shares bought = 400

Amount invested = 400 \times 24 = 9600 \ Rs.

Income from the shares = 400 \times 20 \times \frac{12}{100} = 960 \ Rs. 

% return on his money = \frac{960}{9600} \times 100 = 10\%

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Question 9: A man buys 400, 20 Rs.  shares at a discount of 20% and receives a return of 12% on his money. Calculate: i) The amount invested by him;  ii) The rate of dividend paid by the company.

Answer:

Nominal Price of the share = 20 \ Rs.

Market Price of the share = 16 \ Rs.

The number of Shares bought = 400

Amount invested = 400 \times 16 = 6400 \ Rs.

Return on investment = \frac{12}{100} \times 6400 = 768 \ Rs.

Let the rate of dividend = x\%

Therefore 400 \times 20 \times \frac{x}{100} = 768 \Rightarrow x = 9.6\%

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Question 10: A company, with 10,000 shares of Rs. 100 each, declares an annual dividend of 5%. i) What is the total amount of dividend paid by the company? ii) What should be the annual income of a man who has 72 shares in the company?  iii) If he received only 4% of his investment, find the price he paid for each share.

Answer:

Annual Dividend = 10000 \times 100 \times \frac{5}{100} = 50000 \ Rs.

Annual income of the man = 72 \times 100 \times \frac{5}{100} = 360 \ Rs.

Let the price of the share he bought was x

Therefore the investment = 72x

Hence 72x \times \frac{4}{100} = 360 \Rightarrow x = 125 \ Rs.

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Question 11: A lady holds 1800, Rs. 100 shares of a company that pays 15% dividend annually. Calculate her annual dividend. If she had bought these shares at 40% premium, what is the return she gets as percent on her investment, Give your answer to the nearest integer.

Answer:

Annual dividend = 1800 \times 100 \times \frac{15}{100} = 27000 \ Rs.

Investment = 1800 \times 140 = 252000 \ Rs.

% return = \frac{27000}{252000} \times 100 = 10.71\%

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Question 12: man invests Rs. 11200 in a company paying 6% per annum when its Rs. 100 shares can be bought for Rs. 140. Find; i) His annual dividend  ii) His % return on his investment

Answer:

Number of shares bought = \frac{11200}{140} = 80

Annual dividend = 80 \times 100 \times \frac{6}{100} = 480

Percentage return = \frac{480}{11200} \times 100 = 4.29\%

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Question 13: A person has 60 shares of Nominal Value Rs. 100 and sells them when they are at a premium of 60% he invests the proceeds in shares of nominal value Rs. 50, quoted at 4% discount, and paying 18% dividend annually. Calculate; i) The sale proceeds;  ii) The number of shares he buys and iii) His annual dividend from the shares.

Answer:

Initial Investment = 60 \times 100 = 6000 \ Rs.

Sale Proceeds = 60 \times 160 = 9600 \ Rs.

New Investment is at Rs. 48 per share

Number of shares bought = \frac{9600}{48} = 200

Annual dividend = 200 \times 50 \times \frac{18}{100} = 1800 \ Rs. 

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Question 14: A company with 10,000 shares of nominal value Rs. 100 declares an annual dividend of 8% to the shareholders. i) Calculate the total amount of dividend paid by the by the company ii) A man had bought 90 shares of the company at Rs. 150 per share. Calculate the dividend he receives and the percentage of the return on his investment.

Answer:

Total dividend paid = 10000 \times 100 \times \frac{8}{100} = 80000 \ Rs.  

The dividend man will receive = 90 \times 100 \times \frac{8}{100} = 720 \ Rs. 

% return on his investment = \frac{720}{90 \times 150} \times 100 = 5.33\% 

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Question 15: Which is the better investment: 16% Rs. 100 shares at 80 or 20% Rs. 100 shares at 120?

Answer:

First Investment

Dividend on 16% Rs. 100 shares at 80 = 100 \times 100 \times \frac{16}{100} = 1600 Rs. 

Investment = 100 \times 80 = 8000 Rs. 

% return = \frac{1600}{8000} \times 1000 = 20\% 

Second Investment

Dividend on 20% Rs. 100 shares at 100 = 100 \times 100 \times \frac{20}{100} = 2000 Rs. 

Investment = 100 \times 120 = 12000 Rs. 

% return = \frac{2000}{12000} \times 1000 = 16.67\%

Hence the first investment is better.

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Question 16: A man has a choice to invest in 200 Rs. shares of two firms at Rs. 120 or at 132. The first firm pays a dividend of 5% per annum and the second firm pays a dividend of 6% per annum, Find: i) Which company is giving a better return.  ii) If a man invests Rs. 26,400 with each firm, how much will be the difference between the annual return from the two firms.

Answer:

First Company

Dividend earned = 100 \times 200 \times \frac{5}{100} = 1000 \ Rs.

Investment = 100 \times 120 = 12000 \ Rs.

% return = \frac{1000}{12000} \times 100 = 8.33\%

Return on investment of Rs. 26400 = \frac{26400}{120} \times 200 \times\frac{5}{100} = 2200 \ Rs. 

Second Company

Dividend earned = 100 \times 200 \times \frac{6}{100} = 1200 \ Rs.

Investment = 100 \times 132 = 13200 \ Rs.

% return = \frac{1200}{13200} \times 100 = 9.09\%

Return on investment of Rs. 26400 = \frac{26400}{132} \times 200 \times\frac{6}{100} = 2400 \ Rs. 

Therefore the Second company gives a better return.

Difference between the annual return = 200 Rs.

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Question 17: A man bought 360, 10 Rs. shares of a company, paying 12% per annum. He sold the shares when their price rose to Rs. 21 per shares and invested the proceeds in 5 rupees shares paying 4.5% per annum at Rs. 3.50 per share. Find the annual change in his income.

Answer:

First Investment

Dividend income = 360 \times 10 \times \frac{12}{100} = 432 \ Rs. 

Second Investment

Dividend income = \frac{360  \times 21}{3.50} \times 5 \times \frac{4.5}{100} = 1177.2 \ Rs. 

Hence difference in income = 1177.2 - 432 = 745.2 \ Rs.  

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Question 18: A man sold 400 (Rs. 20) shares of a company, paying 5% at Rs.18 and invested the proceeds in (Rs. 10) shares of another company paying 7% at Rs. 12. How many Rs.10 shares did he buy and What was the change in his income?

Answer:

Income from first investment = 400 \times 20 \times \frac{5}{100} = 4000 \ Rs.  

No of Rs. 10 shares bought   = \frac{400 \times 18}{12} = 600  

Dividend income = 600 \times 10 \times \frac{7}{100} = 4200 \ Rs.  

Hence the difference = 200 \ Rs.  

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Question 19: Two brothers A and B invests Rs. 16,000 each in buying shares of two companies. A buys 3% 100 Rs.  shares at 80 and B buys 10 Rs. shares at par. If they both receive equal dividend at the end of the year, find the rate percent of the dividend received by B.

Answer:

Brother A

Dividend = \frac{16000}{80} \times 100 \times \frac{3}{100} = 600 \ Rs.  

Brother B

Dividend = 600 Rs.

  \frac{16000}{10} \times 10 \times \frac{x}{100} = 600 \Rightarrow x = 3.75\%  

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Question 20: 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:

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

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

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

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Question 21: A person invested Rs. 19,200 in 15% Rs. 100 shares at 20% discount. After a year She sold these shares at Rs. 90 each and invested the proceeds (including her dividend) in 20%, Rs. 50 shares at Rs. 42. Find: i) The number of shares he buys. ii) The dividend he receives annually;  iii) The rate of interest he gets on his money.

Answer:

First Investment

Nominal Price of the share = 100 \ Rs.

Market Price of the share = 80 \ Rs.

Number of shares = \frac{19200}{80} = 240

Dividend Income = 240 \times 100 \times \frac{15}{100} = 3600 \ Rs. 

Rate of interest = \frac{3600}{19200} \times 100 = 18.75\% 

Second Investment

Nominal Price of the share $latex = 50 \ Rs.

Market Price of the share $latex = 42 \ Rs.

Number of shares = \frac{240 \times 90 + 3600}{42} = 600

Dividend Income = 600 \times 50 \times \frac{20}{100} = 6000 \ Rs. 

Rate of interest = \frac{6000}{25200} \times 100 = 23.08\% 

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Question 22: A person invested Rs. 19,200 in 15% Rs. 100 shares at 20% premium. After a year She sold these shares at Rs. 140 each and invested the proceeds (including her dividend)  in 20%, Rs. 20 shares at Rs. 16. Find: i) dividend for the first year ii) annual income in the second year, iii) % change in the return on her original investment.

Answer:

First Investment

Nominal Price of the share = 100 \ Rs.

Market Price of the share = 120 \ Rs.

Number of shares = \frac{19200}{120} = 160

Dividend Income = 160 \times 100 \times \frac{15}{100} = 2400 \ Rs. 

Rate of interest = \frac{2400}{19200} \times 100 = 12.5\% 

Second Investment

Nominal Price of the share $latex = 20 \ Rs.

Market Price of the share $latex = 16 \ Rs.

Number of shares = \frac{160 \times 140 + 2400}{16} = 1550

Dividend Income = 1550 \times 20 \times \frac{20}{100} = 6200 \ Rs. 

Rate of interest = \frac{6200}{24800} \times 100 = 25\% 

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