Maharashtra Board Class 11 Maths Part 2 Chapter 9 Commercial Mathematics 9.7 Solutions

Commercial Mathematics Class 11 Commerce Maths 2 Chapter 9 Exercise 9.7 Answers Maharashtra Board

Std 11 Maths 2 Exercise 9.7 Solutions Commerce Maths

Question 1. Shantanu has a choice to invest in 10 shares of two firms at 13 or at 16. If the first firm pays a 5% dividend and the second firm pays a 6% dividend per annum, find:
(i) Which firm is paying better?
(ii) If Shantanu invests equally in both the firms and the difference between the return from them is Rs. 30. Find how much, in all, does he invest.
Answer:
Solution:
(i) For firm 1:
Face value of the share (F.V.) = Rs. 10
Market value of the share (M.V.) = Rs. 13
Dividend = 5%
\( \therefore \) Annual income from the share = \( \frac{5}{100} \times 10 = 0.5 \)
Profit percentage = \( \frac{\text{Annual income}}{\text{Market value}} \times 100 \)
= \( \frac{0.5}{13} \times 100 \)
= \( \frac{50}{13} \)
\( \approx 3.85\% \)
For firm 2:
Face value of the share (F.V.) = Rs. 10
Market value of the share (M.V.) = Rs. 16
Dividend = 5%
\( \therefore \) Annual income from the share = \( \frac{6}{100} \times 10 = 0.6 \)
Profit percentage = \( \frac{\text{Annual income}}{\text{Market value}} \times 100 \)
= \( \frac{0.6}{16} \times 100 \)
= \( \frac{60}{16} \)
= \( 3.75\% \)
Since, the profit percentage from firm 1 > profit percentage from firm 2, the first firm is paying better.
(ii) Let 'X' be the amount Shantanu invests in each of the firms.
Given that difference between the return from them is Rs. 30, we have
\( \frac{50}{13} X - \frac{60}{16} X = 30 \)
...[From (i) and (ii)]
\( \therefore X \left( \frac{50}{13} - \frac{60}{16} \right) = 30 \times 100 \)
\( \therefore X \left( \frac{50 \times 16 - 60 \times 13}{13 \times 16} \right) = 3000 \)
\( \therefore X \left( \frac{800 - 780}{13 \times 16} \right) = 3000 \)
\( \therefore X \frac{20}{13 \times 16} = 3000 \)
\( X = \frac{3000 \times 13 \times 16}{20} \)
\( \therefore X = 31,200 \)
In all, Shantanu invests = \( 2X \)
= \( 2 \times 31,200 \)
= Rs. 62,400/-
In simple words: To find which firm is better, we calculate the profit percentage for each firm based on their dividend and market value. Firm 1 yields a higher profit percentage. For the total investment, we use the given difference in returns to solve for the individual investment amount (X) in each firm, then double it to get the total.

🎯 Exam Tip: When comparing investments, always calculate the profit percentage to determine which option offers a better return. Ensure all calculations for annual income and market value are correct, especially when dealing with premiums or discounts.

Question 2. A dividend of 9% was declared on 100 shares selling at a certain price in the stock market. If the rate of return is 7.5% calculate
(i) The market price of each share, and
(ii) The amount to be invested to obtain an annual dividend of Rs. 630.
Answer:
Solution:
(i) Given that,
Face value of the share (F.V) = Rs. 100
Dividend = 9%
Rate of return = 7.5%
Annual income from the share = \( \frac{9}{100} \times 100 = \text{Rs. } 9 \)
Rate of return = \( \frac{\text{Annual income}}{\text{Market price}} \times 100 \)
\( 7.5 = \frac{9}{\text{Market price}} \times 100 \)
\( \therefore \) Market price = \( \frac{900}{7.5} \)
= Rs. 120
\( \therefore \) The market price of the share is 120.
(ii) Let 'X' be the amount to be invested to obtain an annual dividend of Rs. 630.
\( \therefore 7.5\% \) of X is 630
\( \therefore \frac{7.5}{100} \times X = 630 \)
\( \therefore X = \frac{630 \times 100}{7.5} \)
\( \therefore X = 8400 \)
\( \therefore \) Rs. 8400 need to be invested to obtain an annual dividend of 630.
In simple words: First, we find the market price of one share using the given dividend percentage and rate of return. Second, we determine the total investment needed to achieve a specific annual dividend by setting up a proportion based on the rate of return.

🎯 Exam Tip: Clearly distinguish between dividend percentage and rate of return. The dividend is based on face value, while the rate of return is based on the market price or total investment. Always use the correct base value for each calculation.

Question 3. Nilesh has the option of investing his money in 8% 10 shares at a premium of 3.50 or 7% 100 shares at a premium of 20%. Which of the two investments will be more profitable for him?
Answer:
Solution:
For share 1:
Face value of the share (F.V.) = Rs. 10
Premium = Rs. 3.5
\( \therefore \) Market value of the share (M.V.) = \( 10 + 3.5 = \text{Rs. } 13.5 \)
Dividend = 8%
\( \therefore \) Annual income from the share = \( \frac{8}{100} \times 10 = 0.8 \)
Profit percentage = \( \frac{\text{Annual income}}{\text{Market value}} \times 100 \)
= \( \frac{0.8}{13.5} \times 100 \)
= \( \frac{800}{135} \)
= \( 5.93\% \)
For share 2:
Face value of the share (F.V.) = Rs. 100
Premium = 20%
\( \therefore \) Market value of the share (M.V.) = \( 100 + \left( \frac{20}{100} \times 100 \right) = \text{Rs. } 120 \)
Dividend = 7%
Annual income from the share = \( \frac{7}{100} \times 100 = \text{Rs. } 7 \)
Profit percentage = \( \frac{\text{Annual income}}{\text{Market value}} \times 100 \)
= \( \frac{7}{120} \times 100 \)
\( \approx 5.833\% \)
Since, profit percentage from share 1 > profit percentage from share 2, investing in the first kind of shares will be more profitable for Nilesh.
In simple words: To compare the profitability of two investments, we calculate the profit percentage for each share type. This is done by first finding the market value and annual income per share, then dividing the annual income by the market value and multiplying by 100. The investment with the higher profit percentage is more profitable.

🎯 Exam Tip: When comparing multiple investment options, always calculate the 'Rate of Return' or 'Profit Percentage' for each, as it provides a standardized measure of profitability. Remember that premium affects the market value of the share.

Question 4. Sudhakar invests Rs. 1344 in buying shares of face value 24 selling at a 12% premium. The dividend on the shares is 15% per annum. Calculate
(i) The number of shares Sudhakar buys, and
(ii) The dividend he receives annually.
Answer:
Solution:
Given that,
Face value of the share (F.V.) = Rs. 24
Premium = 12%
\( \therefore \) Market value of the share (M.V.) = \( 24 + \left( \frac{12}{100} \times 24 \right) = \text{Rs. } 26.88 \)
(i) Sudhakar invests Rs. 1344 in the shares
\( \therefore \) Number of shares purchased by Sudhakar = \( \frac{1344}{26.88} = 50 \)
\( \therefore \) Sudhakar buys 50 shares.
(ii) Dividend on the share = 15%
Annual income on one share = \( \frac{15}{100} \times 24 = 3.6 \)
\( \therefore \) The total dividend he receives annually = \( 50 \times 3.6 = \text{Rs. } 180 \)
\( \therefore \) Sudhakar receives Rs. 180 as his annual dividend.
In simple words: First, calculate the market value of a share by adding the premium to the face value. Then, divide the total investment by the market value per share to find the number of shares bought. Finally, calculate the dividend per share based on the face value and dividend rate, and multiply it by the number of shares to get the total annual dividend.

🎯 Exam Tip: When calculating market value with a premium, ensure you add the premium *amount* (percentage of face value) to the face value. Dividend is always calculated on the face value, not the market value.

Question 5. Sameer invests Rs. 5625 in a company paying 7% per annum when the share of Rs. 10 stands for Rs. 12.50. Find Sameer's income from this investment. If he sells 60% of these shares of Rs. 10 each, find his gain or loss in this transaction.
Answer:
Solution:
Given:
Face value of the share (F.V.) = Rs. 10
Market value of the share (M.V.) = Rs. 12.5
Amount invested in shares = Rs. 5625
\( \therefore \) Number of shares purchased by Sameer = \( \frac{5625}{12.5} = 450 \)
Dividend = 7%
Annual income from one share = \( \frac{7}{100} \times 10 = \text{Rs. } 0.7 \)
\( \therefore \) Sameer's income from this investment = number of shares \( \times \) annual income from one share
= \( 450 \times 0.7 \)
= Rs. 315
Sameer sells 60 % of these shares = \( \frac{60}{100} \times 450 = 270 \) shares
Sameer purchased these shares at 12.5 per share.
\( \therefore \) Purchase price for these shares = \( 270 \times 12.5 = \text{Rs. } 3375 \)
If he sells these shares at 10 per share, he would receive \( 270 \times 10 = \text{Rs. } 2700 \)
\( \therefore \) In this transaction, Sameer would incur a loss of \( 3375 - 2700 = \text{Rs. } 675 \)
In simple words: First, calculate the number of shares Sameer bought by dividing his total investment by the market value per share. Then, find his annual income by multiplying the number of shares by the dividend per share. Next, calculate the number of shares sold (60% of total) and their original purchase price. Finally, compare this purchase price to the selling price of those shares to determine the gain or loss.

🎯 Exam Tip: This question has two distinct parts: calculating annual income and determining gain/loss from selling shares. Ensure you calculate the income based on the face value and the gain/loss based on the market price (purchase price vs. selling price).

Question 6. Geeta buys 100 shares of a company that pays a 15% dividend. She buys the shares at a price from the market that gives her a 10% return on her investment. At what price did she buy each share?
Answer:
Solution:
Given that,
Face value of the share (F.V.) = Rs. 100
Dividend = 15%
\( \therefore \) Annual income from the share = \( \frac{15}{100} \times 100 = \text{Rs. } 15 \)
Rate of return on investment = 10%
Rate of return = \( \frac{\text{Annual income}}{\text{Market price}} \times 100 \)
\( \therefore 10 = \frac{15}{\text{Market price}} \times 100 \)
\( \therefore \) Market price = \( \frac{1500}{10} = 150 \)
\( \therefore \) Geeta bought each share from the market at Rs. 150.
In simple words: First, determine the annual income per share using the face value and dividend rate. Then, use the given rate of return on investment and the annual income per share to calculate the market price at which each share was bought.

🎯 Exam Tip: Understand that annual income is calculated on the face value, while the rate of return is based on the market price (the actual investment). Use the rate of return formula to work backward and find the market price.

Question 7. Tejas invests in 9% 100 shares at 145 but Shail invests in 7% 100 shares at 116. Whose investment is better?
Answer:
Solution:
Investment of Tejas:
Given that, the Face value of the share (F.V.) = Rs. 100
The market value of the share (M.V.) = Rs. 145
Dividend = 9%
Annual income from the share = \( \frac{9}{100} \times 100 = 9 \)
Rate of return = \( \frac{\text{Annual income}}{\text{Market value}} \times 100 \)
= \( \frac{9}{145} \times 100 \)
= \( \frac{900}{145} \)
\( \approx 6.2\% \)
Investment of Shail:
Face value of the share (F.V.) = Rs. 100
Market value of the share (M.V.) = Rs. 116
Dividend = 7%
Annual income from the share = \( \frac{7}{100} \times 100 = \text{Rs. } 7 \)
Rate of return = \( \frac{\text{Annual income}}{\text{Market value}} \times 100 \)
= \( \frac{7}{116} \times 100 \)
\( \approx 6.03\% \)
Since the rate of return for Tejas's investment is greater than that for Shail's, Tejas's investment is better.
In simple words: To compare two investments, calculate the annual income per share for each, based on the face value and dividend rate. Then, compute the rate of return for each investment by dividing the annual income by the market value and multiplying by 100. The investment with the higher rate of return is considered better.

🎯 Exam Tip: Always calculate the 'Rate of Return' for each investment to make a fair comparison of profitability, as this metric considers both the income and the actual market price paid for the shares.

Question 8. A 6% share yields 8%. Find the market value of a 100 share.
Answer:
Solution:
Given that,
Face value of the share = Rs. 100
Dividend = 6%
Yield = 8%
Annual income on the share = \( \frac{6}{100} \times 100 = 6 \)
Yield = \( \frac{\text{Annual income}}{\text{Market value}} \times 100 \)
\( 8 = \frac{6}{\text{Market value}} \times 100 \)
\( \therefore \) Market value = \( \frac{600}{8} \)
= 75
\( \therefore \) The market value of the share = Rs. 75
In simple words: First, calculate the annual income from the share using its face value and dividend rate. Then, use the given yield percentage and the calculated annual income to find the market value of the share.

🎯 Exam Tip: Understand that "yield" is another term for "rate of return" and is calculated based on the market value, while the dividend is based on the face value. This relationship is key to finding the unknown market value.

Question 9. Ashwini bought 40 shares at a premium of 40%. Find the income, if Ashwini invests 14,000 in these shares and receives a dividend at the rate of 8% on the nominal value of the shares.
Answer:
Solution:
Given,
Face value of the shares (F.V.) = Rs. 40
Premium = 40%
Market value of the shares (M.V.) = \( 40 + \left( 40 \times \frac{40}{100} \right) \)
= \( 40 + 16 \)
= Rs. 56
Ashwini invests Rs. 14000 in these shares
\( \therefore \) Number of shares bought by Ashwini = \( \frac{\text{Amount Invested}}{\text{Market value of one share}} \)
= \( \frac{14000}{56} \)
= 250
Dividend = 8%
\( \therefore \) Annual income on one share = \( \frac{8}{100} \times 40 = 3.2 \)
\( \therefore \) Income of Ashwini on 250 shares = \( 250 \times 3.2 = \text{Rs. } 800 \)
\( \therefore \) Ashwini earns 800 on her investment.
In simple words: First, calculate the market value of each share by adding the premium to its face value. Then, determine the total number of shares Ashwini bought by dividing her total investment by the market value per share. Finally, calculate the annual income per share based on the face value and dividend rate, and multiply it by the total number of shares to find her total annual income.

🎯 Exam Tip: Be careful to calculate the market value correctly when a premium is involved. Remember that the dividend is always based on the nominal (face) value of the share, not the market value or the premium.

Question 10. Mr. Rutvik invests Rs. 30,000 in buying shares of a company that pays a 12% dividend annually on 100 shares selling at a premium of Rs. 50. Find
(i) The number of shares bought Mr. Rutvik and
(ii) His annual income from the shares.
Answer:
Solution:
Given that,
Face value of a share (F.V.) = Rs. 100
Premium = Rs. 50
\( \therefore \) Market value of a share (M.V.) = \( 100 + 50 = \text{Rs. } 150 \)
Dividend = 12%
Mr. Rutvik invests Rs. 30,000 in the shares.
(i) Number of shares bought by Mr. Rutvik = \( \frac{\text{Amount invested}}{\text{Market value}} \)
= \( \frac{30000}{150} \)
= 200
(ii) Dividend on the share = 12%
\( \therefore \) Annual income from one share = \( \frac{12}{100} \times 100 = \text{Rs. } 12 \)
\( \therefore \) His annual income from shares = number of shares \( \times \) income from one share
= \( 200 \times 12 \)
= Rs. 2400
In simple words: First, calculate the market value of each share by adding the premium to the face value. Then, divide the total investment by the market value per share to find the number of shares bought. Finally, calculate the annual income per share based on the face value and dividend rate, and multiply it by the total number of shares to get the total annual income.

🎯 Exam Tip: Pay close attention to distinguishing between face value (used for dividend calculation) and market value (used for investment and number of shares bought). A premium increases the market value of the share.

Question 11. Rasika bought 40 shares at a discount of 40%. Find the income, if she invests 12,000 in these shares and receives a dividend at the rate of 11% on the nominal value of the shares.
Answer:
Solution:
Given,
Face value of the shares (F.V.) = Rs. 40
Discount = 40%
\( \therefore \) Market value of the shares (M.V.) = \( 40 - \left( 40 \times \frac{40}{100} \right) \)
= \( 40 - 16 \)
= Rs. 24
Rasika invests Rs. 12,000 in these shares.
\( \therefore \) Number of shares bought by Rasika = \( \frac{\text{Amount invested}}{\text{Market value of one share}} \)
= \( \frac{12000}{24} \)
= 500
Dividend = 11%
\( \therefore \) Annual income on one share = \( \frac{11}{100} \times 40 = \text{Rs. } 4.4 \)
\( \therefore \) Rasika's income on 200 such shares = \( 500 \times 4.4 = \text{Rs. } 2200 \)
\( \therefore \) Rasika earns 2200 from her investment.
In simple words: First, calculate the market value of each share by subtracting the discount from its face value. Then, divide the total investment by the market value per share to find the number of shares bought. Finally, calculate the annual income per share based on the face value and dividend rate, and multiply it by the total number of shares to find her total annual income.

🎯 Exam Tip: When a discount is applied, subtract the discount amount (percentage of face value) from the face value to get the market value. Always remember that dividends are calculated on the face value, not the discounted market value.

Question 12. Nisha invests 15,840 in buying shares of nominal value 24 selling at a premium of 10%. The company pays a 15% dividend annually. Find
(i) The dividend she receives annually, and
(ii) The rate of return from her investment.
Answer:
Solution:
Given that,
Face value of the share (F.V.) = Rs. 24
Premium = 10%
\( \therefore \) Market value of the share (M.V.) = \( 24 + \left( 24 \times \frac{10}{100} \right) \)
= \( 24 + 2.4 \)
= Rs. 26.4
Dividend = 15%
\( \therefore \) Annual income on the share = \( \frac{15}{100} \times 24 = 3.6 \)
Nisha invests Rs. 15,840 in these shares.
\( \therefore \) Number of shares bought by Nisha
= \( \frac{\text{Amount invested}}{\text{Market value of one share}} \)
= \( \frac{15840}{26.4} \)
= 600
(i) Annual dividend received by Nisha = Number of shares \( \times \) annual income from one share
= \( 600 \times 3.6 \)
= Rs. 2160
(ii) Rate of return from the investment
= \( \frac{\text{Annual dividend}}{\text{Amount invested}} \times 100 \)
= \( \frac{2160}{15840} \times 100 \)
= \( 13.64\% \)
In simple words: First, calculate the market value of each share by adding the premium to its nominal value. Then, determine the number of shares Nisha bought by dividing her total investment by the market value per share. Next, calculate the annual income per share based on the nominal value and dividend rate to find her total annual dividend. Finally, calculate the rate of return by dividing the total annual dividend by the total investment and multiplying by 100.

🎯 Exam Tip: Remember to calculate the market value accurately using the premium. The annual dividend is based on the nominal (face) value, while the rate of return is calculated using the total annual dividend and the total amount invested (based on market value).

Question 13. Ashutosh buys 80, Rs. 100 shares at a discount of 20% and receives a return of 12% on his money. Calculate
(i) The amount invested by Ashutosh.
(ii) The rate of dividend paid by the company.
Answer:
Solution:
Given
Face value of the shares (F.V.) = Rs. 100
Discount = 20%
\( \therefore \) Market value of the shares (M.V.) = \( 100 - \left( 100 \times \frac{20}{100} \right) = \text{Rs. } 80 \)
(i) Amount invested by Ashutosh = number of shares \( \times \) market value of the shares
= \( 80 \times 80 \)
= Rs. 6400
(ii) Ashutosh receives a return of 12% on his money.
\( \therefore \) Ashutosh's income from shares = \( \frac{12}{100} \times 6400 = \text{Rs. } 768 \)
\( \therefore \) Ashutosh's annual income from one share = \( \frac{768}{80} = \text{Rs. } 9.6 \)
Annual income from one share = \( \frac{\text{Dividend}}{100} \times \text{Face value} \)
\( \therefore 9.6 = \frac{\text{Dividend}}{100} \times 100 \)
\( \therefore \) Rate of dividend = 9.6%
In simple words: First, calculate the market value of each share by subtracting the discount from its face value. Then, find the total amount invested by multiplying the number of shares by the market value per share. Second, calculate Ashutosh's total income based on his 12% return on investment. From this total income, find the income per share. Finally, use the income per share and the face value to determine the rate of dividend paid by the company.

🎯 Exam Tip: Differentiate between the "rate of return" (calculated on total investment/market value) and the "rate of dividend" (calculated on face value). Work step-by-step to isolate the required values using the correct base for each percentage.

Question 14. Vaishnavi bought 1000, Rs. 100 shares from the stock market carrying 8% dividend quoted at 130. A few days later the market value of the shares went up by 10%. Vaishnavi sold all her shares. What was her total income from this transaction?
Answer:
Solution:
Given that,
Face value of the shares (F.V.) = Rs. 100
The market value of the shares (M.V.) = Rs. 130
Dividend = 8%
Income from the each share = \( \frac{8}{100} \times 100 = \text{Rs. } 8 \)
Number of shares bought by Vaishnavi = 1000
\( \therefore \) Vaishnavi's income from dividend = \( 1000 \times 8 = \text{Rs. } 8000 \)
The price of the shares went up by 10%
New market value of the shares = \( 130 + \left( 130 \times \frac{10}{100} \right) = 143 \)
Vaishnavi sold the shares at Rs. 143 which she bought at Rs. 130 each.
\( \therefore \) Vaishnavi's profit on one share = \( 143 - 130 = \text{Rs. } 13 \)
\( \therefore \) Vaishnavi's profit after selling all her shares = \( 1000 \times 13 = \text{Rs. } 13,000 \)
Vaishnavi's total income from this transaction = Income from dividend + income from sale of shares
= \( 8,000 + 13,000 \)
= Rs. 21,000
\( \therefore \) Vaishnavi's total income from this transaction was 21,000.
In simple words: First, calculate the total dividend income by multiplying the number of shares by the dividend per share (based on face value). Then, determine the new market value after the 10% increase. Calculate the profit per share from selling by subtracting the original market value from the new market value, and multiply by the total shares to get the profit from sale. Finally, add the dividend income and the profit from sale to find the total income from the transaction.

🎯 Exam Tip: Total income from a share transaction includes both the dividend received (calculated on face value) and the capital gain/loss from selling the shares (calculated on market price differences). Ensure to account for both components.

Question 15. Mr. Dinesh invests Rs. 20,800 in 6% Rs. 100 shares at Rs. 104, and Rs. 14,300 in 10.5% Rs. 100 shares at Rs. 143. What will be his annual income from the shares?
Answer:
Solution:
For 1st kind of shares,
Face value of shares (F.V.) = Rs. 100
Dividend = 6%
\( \therefore \) Annual income from one share = \( \frac{6}{100} \times 100 = \text{Rs. } 6 \)
Market value of the share (M.V.) = Rs. 104
Total amount invested = Rs. 20,800
\( \therefore \) Number of shares = \( \frac{\text{Amount invested}}{\text{Market value}} \)
= \( \frac{20,800}{104} \)
= 200
\( \therefore \) Total income from 1st kind of shares = \( 200 \times 6 = \text{Rs. } 1200 \)
For 2nd kind of shares,
Face value of shares (F.V.) = Rs. 100
Dividend = 10.5%
\( \therefore \) Annual income from one share = \( \frac{10.5}{100} \times 100 = \text{Rs. } 10.5 \)
Market value of the share (M.V.) = Rs. 143
Total amount invested = Rs. 14300
\( \therefore \) Number of shares = \( \frac{\text{Amount invested}}{\text{Market value}} \)
= \( \frac{14300}{143} \)
= 100
\( \therefore \) Total income from 2nd kind of shares = \( 100 \times 10.5 = \text{Rs. } 1050 \)
\( \therefore \) Total annual income of Dinesh from both these shares = \( 1200 + 1050 = \text{Rs. } 2250 \)
In simple words: For each type of share, calculate the annual income per share (based on face value and dividend rate). Then, determine the number of shares bought by dividing the invested amount by the market value per share. Multiply the number of shares by the income per share to get the total income from that type of share. Finally, add the incomes from all types of shares to find the total annual income.

🎯 Exam Tip: Treat each investment separately to calculate its individual income. Remember to use the face value for dividend calculation and the market value to determine the number of shares purchased. Summing the individual incomes gives the total annual income.

Question 16. A company declares a semi-annual dividend of 5%. Daniel has 400 shares of the company. If Daniel's annual income from the shares is Rs. 1,000, find the face value of each share.
Answer:
Solution:
Given that,
Semi-annual dividend = 5%
\( \therefore \) Annual dividend = 10%
Number of shares with Daniel = 400
Daniel's annual income from the shares = Rs. 1000
\( \therefore \) Annual income from one share = \( \frac{1000}{400} = \text{Rs. } 2.5 \)
But annual income from one share = \( \frac{\text{Annual dividend}}{100} \times \text{Face value} \)
\( \therefore 2.5 = \frac{10}{100} \times \text{Face value of the share} \)
\( \therefore \) Face value of the share = Rs. 25
In simple words: First, convert the semi-annual dividend to an annual dividend rate. Then, divide Daniel's total annual income by the number of shares he owns to find the annual income per share. Finally, use this annual income per share along with the annual dividend rate to calculate the face value of each share.

🎯 Exam Tip: Be cautious about semi-annual vs. annual dividend rates; always convert to an annual rate for consistency. The formula for annual income per share (dividend rate applied to face value) is crucial for finding the unknown face value.

Question 17. Bhargav buys 400, Rs. 20 shares at a premium of 4 each and receives a dividend of 12%. Find
(i) The amount invested by Bhargav.
(ii) His total income from the shares.
(iii) Percentage return on his money.
Answer:
Solution:
Given that,
Face value of the shares (F.V.) = Rs. 20
Premium = Rs. 4
\( \therefore \) Market value of the shares (M.V.) = Rs. 24
Dividend = 12%
\( \therefore \) Annual income from the share = \( \frac{12}{100} \times 20 = \text{Rs. } 2.4 \)
Bhargav buys 400 shares
(i) The amount invested by Bhargav = number of shares \( \times \) market value
= \( 400 \times 24 \)
= Rs. 9600
(ii) Bhargav's income from the shares = number of shares \( \times \) annual income from one share
= \( 400 \times 2.4 \)
= Rs. 960
(iii) Percentage return on Bhargav's money
= \( \frac{\text{Total annual income}}{\text{Total amount invested}} \times 100 \)
= \( \frac{960}{9600} \times 100 \)
= 10%
\( \therefore \) Bhargav gets 10% as the rate of return on his money.
In simple words: First, calculate the market value of each share by adding the premium to the face value. Then, find the total investment by multiplying the number of shares bought by this market value. Next, calculate the annual income per share (based on face value and dividend rate) and multiply it by the total number of shares to find the total income. Finally, calculate the percentage return by dividing the total annual income by the total amount invested and multiplying by 100.

🎯 Exam Tip: This question covers all core concepts: market value calculation (with premium), total investment, total annual income, and percentage return. Ensure each step is accurate, remembering that dividend is on face value while investment and return are on market value.

Question 18. Anil buys 350 Rs. 100 shares of a company at a premium of 20% from the market. The company pays 12% dividend annually. Find
(i) the investment made by Anil,
(ii) his annual income from the shares, and
(iii) the rate of return from the shares.
Answer:
Solution:
Given that,
Face value of shares (F.V.) = Rs. 100
Premium = 20%
\( \therefore \) Market value of shares (M.V.) = \( 100 + \left( \frac{20}{100} \times 100 \right) = \text{Rs. } 120 \)
Dividend = 12%
\( \therefore \) Annual income from one share = \( \frac{12}{100} \times 100 = \text{Rs. } 12 \)
Anil buys 350 shares.
(i) Amount invested by Anil = number of shares \( \times \) market value
= \( 350 \times 120 \)
= Rs. 42,000
(ii) Anil's annual income from the shares = number of shares \( \times \) annual income from one share
= \( 350 \times 12 \)
= Rs. 4200
(iii) Rate of return from shares
= \( \frac{\text{Total annual income}}{\text{Total annual invested}} \times 100 \)
= \( \frac{4200}{42000} \times 100 \)
= 10%
\( \therefore \) The rate of return from Anil's shares is 10%.
In simple words: First, calculate the market value of each share by adding the 20% premium to its face value. Then, determine the total investment by multiplying the number of shares bought by this market value. Next, calculate the annual income per share based on the face value and dividend rate, and multiply it by the total shares to find the total annual income. Finally, calculate the rate of return by dividing the total annual income by the total investment and multiplying by 100.

🎯 Exam Tip: Remember that investment is always based on the market value (which includes premium), while dividend calculation relies on the face value. The rate of return shows the profitability relative to the actual money invested.