Example 1: How much money should be invested to purchase Rs. 6000 of 5% stock at 106¾ brokerage being ¼%?
Sol: Total price paid to buy one share = 106¾ + ¼ = Rs. 107.
Stock needed = Rs. 6000. Investment = 6000×107/100= Rs. 6420
Example 2: Money is worth 4%. At what price should the stock which pays 5 percent be quoted?
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Sol: The simple logic applicable is that the 5% the man earns should be 4% of his investment. In order to earn Rs. 4, one can invest Rs. 100
In order to earn Rs. 5, one can invest Rs. 100 ×(5/4) = Rs. 125. Hence the market price of the stock should be Rs. 125.
Example 3: How much should a person invest in 5% stock at Rs. 114 to get a net income of Rs. 300 a year after paying an income tax of 5 paise in a rupee?
Sol: Gross income the person will get on Rs. 114 = Rs. 5. Tax to be paid on Rs. 5 = Rs. 0.25.
⇒ Net income = 5 – 0.25 = Rs. 4.75. Now apply the chain rule.
In order to get an income of Rs. 4.75, one should invest Rs. 114;
In order to get an income of Rs. 300, one should invest 300 ×(114/4.475) = Rs. 7200.
Example 4: Find the annual income obtained by investing Rs 3000 in 5% debentures of face value Rs 100 at Rs 125?
Sol: The number of debentures purchased = Rs. 3000/125
One debenture will give an income investment of Rs 100 × 5% = Rs 5. So total income = 5 × (3000/125) = Rs 120.
Example 5: A man sells Rs. 6000, 5% stock at 120 and invests the proceeds partly in 6% stock at 105 and partly in 12% stock at 140. He increases his income by Rs. 200. How much was invested in 12% stock at 140?
Sol: The original income that the man was getting was 5 × 6000/100 = Rs 300.
The value of the sales proceeds is Rs 6000 × 120/100 = Rs 7200.
His new income out of this is Rs 300 + 200 = Rs 500.
Let A be the amount invested in 12% stock. So amount invested in 6% stock is (7200 – A).
New income = A × 12/140 + (7200 – A) × 6/105 = 500. Solving we get A = 3100.
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Example 6. How much money should be invested to purchase Rs. 5,650 of 4% stock at 105 4/5 brokerage being 1/5%.
Sol: Total price paid to buy one share = 105 4/5 + 1/5= Rs. 106.
Stock needed = Rs. 5,650.
Investment = 5650 × 106/100 = Rs. 5989.
Example 7. Money is worth 10%. At what price should the stock which pays 11 percent be quoted?
Sol: The simple logic applicable is that the 11% the man earns should be 10% of his investment.
In order to earn Rs. 10, one can invest Rs. 100
In order to earn Rs. 11, one can invest Rs. 100 × (11/10) = Rs. 110. Hence the market price of the stock should be Rs. 110.
Example 8. How much should a person invest in 4% stock at Rs. 97 to get a net income of Rs. 700 a year after paying an income tax of 50 paise in a rupee.
Sol: Gross income the person will get on Rs. 97 = Rs. 4.
Tax to be paid on Rs. 4 = 0.50 Rs.
⇒ Net income = 4 – 0.50 = Rs. 3.50.
Now apply the chain rule.
In order to get an income of Rs. 3.50, one should invest Rs. 97; In order to get an income of Rs. 700, one should invest 700 × (97/3.50) = Rs. 19,400.
Example 9. Find the annual income obtained by investing Rs 3900 in 3% debentures of face value Rs 100 at Rs 130?
Sol: The number of debentures purchased = Rs. 3900/130
One debenture will give an income investment of Rs 100 × 3% = Rs 3. So total income = 3 × 3900/130 = Rs 90.
Example 10. A man sells Rs 4,400, 3% stock at 130 and invests the proceeds partly in 2% stock at 60 and partly in 5% stock at 250. He thereby increases his income by Rs. 8. How much of the sales proceed were invested in each stock?
Sol: The original income that the man was getting was 5 ×(4440/100) = Rs 132.
The value of the sales proceeds is
Rs 4,400 ×(130/100) = Rs 5,720.
His new income out of this is Rs 132 + 8 = Rs 140.
Let A be the amount invested in 2% stock.
So amount invested in 5% stock is 5720 – A.
New income = A ×(2/60) + (5720 – A) × (5/250)= 140.
Solving we get A = 1920.
So money invested in 2% debenture is Rs. 1920 and that in 5% debenture is Rs 4400.