**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?

**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.