Suppose a company needs money. It splits itself into small pieces called shares and sells them to many people. The government does the same with stock. Buyers get a yearly payment in return.
Exam questions on this topic look long. They are not. Only three ideas are used again and again. This article gives the formulas, the shortcuts and five solved examples, each with a line on why the method works.
- Face value is the fixed amount printed on the stock, usually Rs 100.
- Market price is what you actually pay for each Rs 100 of face value.
- Income = rate % × face value. The rate always works on face value, never on market price.
- Cost is the price per Rs 100, scaled up to your face value.
- Return = income ÷ cost × 100. A higher return means a better buy.
- Brokerage is added to the price when buying and subtracted when selling.
What do the words stock, share and face value mean?
What is a stock, and what is a share?
A share is one small part of a company. A stock is a block of such parts, or a loan note issued by the government. Both pay a fixed yearly amount.
In these questions, we treat both the same way. We talk about Rs 100 of stock, and we ask what it pays and what it costs.
Sources: NCERT Class 8 Maths: Comparing Quantities, percentage of a quantity; Practice question: cost of Rs 8000 stock.
What is face value?
Face value is the amount printed on the stock. In most questions, it is Rs 100. It is also called the nominal value or par value.
The yearly payment is worked out on this number only. It never depends on the market price.
Sources: NCERT Class 8 Maths: Comparing Quantities, percentage as a rate.
What is market price, and what do premium and discount mean?
The market price is the amount you pay for Rs 100 of face value on a given day. It can be above or below Rs 100.
If the price is above Rs 100, the stock is at a premium. If it is below, the stock is at a discount. If it equals Rs 100, it is at par.
- At 23 premium means a price of 100 + 23 = Rs 123.
- At 16 discount means a price of 100 − 16 = Rs 84.
- At 84 simply means a price of Rs 84.
Sources: NCERT Class 8 Maths: Comparing Quantities, increase and decrease; Practice question: stock at a premium.
What does the rate of a stock mean?
A 9% stock pays Rs 9 each year for every Rs 100 of face value. This yearly payment is called the dividend or income.
The rate is fixed on the face value. If the market price rises or falls, the dividend does not change.
Sources: NCERT Class 8 Maths: Comparing Quantities, percentage as a rate; Practice question: income from an 8% stock.
Which formulas and shortcuts solve every question?
How do you find the income from a stock?
Multiply the rate by the face value. Income = (rate ÷ 100) × face value.
For Rs 8200 of 8% stock, income = 8 ÷ 100 × 8200 = Rs 656. The market price of 106 is not used here.
Sources: NCERT Class 8 Maths: Comparing Quantities, percentage of a quantity; Practice question: annual income from stock.
How do you find the cost of buying stock?
Multiply the market price by the face value, and divide by 100. Cost = (market price ÷ 100) × face value.
For Rs 8000 of stock at 84, cost = 84 ÷ 100 × 8000 = Rs 6720.
Sources: NCERT Class 8 Maths: Comparing Quantities, finding the whole from a part; Practice question: cost of Rs 8000, 9% stock at 84.
How do you find the rate of return on money invested?
Divide the income by the money spent, then multiply by 100. Return % = (income ÷ cost) × 100.
A 5% stock at 125 pays Rs 5 on every Rs 125 spent. So the return is 5 ÷ 125 × 100 = 4%.
Sources: NCERT Class 8 Maths: Comparing Quantities, percentage as a rate; Practice question: rate of interest on a 5% stock at 125.
Which shortcut works when the income is given and you need the investment?
Use the pair of numbers in the stock name. A 4% stock at 65 pays Rs 4 on every Rs 65 spent.
To earn Rs 128, you need 128 ÷ 4 = 32 such blocks. So you invest 32 × 65 = Rs 2080.
- Investment = (market price ÷ rate) × income wanted.
- Face value bought = (income wanted ÷ rate) × 100.
Sources: NCERT Class 8 Maths: Comparing Quantities, finding the whole from a part; Practice question: investment needed for Rs 128 income.
How does brokerage change the price?
Brokerage is a small fee on each Rs 100 of face value. When you buy, add it to the price. When you sell, subtract it.
So with brokerage of Rs 0.5, a stock at 91 costs Rs 91.5 per Rs 100. A stock sold at 105 with brokerage of Rs 0.25 brings in Rs 104.75.
Sources: NCERT Class 8 Maths: Comparing Quantities, profit, loss and discount; Practice question: cash needed with brokerage.
How do you decide which of two stocks is the better buy?
Find the income earned per rupee spent for each stock. This is the rate divided by the market price.
The stock with the larger answer is better. Compare 6 ÷ 146 = 0.041 with 8.5 ÷ 80 = 0.106. The 8.5% stock at 80 wins.
Sources: NCERT Class 8 Maths: Comparing Quantities, comparing by percentage; Practice question: better of two investments.
Check 1
A 9% stock pays Rs 9 a year on each Rs 100 of face value.
Check 2
If the market price rises, the yearly income from the stock also rises.
Check 3
A stock at 23 premium has a market price of Rs 123.
Check 4
Brokerage is subtracted from the price when you buy.
How do you solve five typical problems step by step?
Example 1: Rs 5000 of 8% stock is bought at 80. Find the cost, the income and the return.
Step 1. Cost = 80 ÷ 100 × 5000 = Rs 4000.
Step 2. Income = 8 ÷ 100 × 5000 = Rs 400.
Step 3. Return = 400 ÷ 4000 × 100 = 10%.
Check. 10% of Rs 4000 is Rs 400, which matches the income.
Why this works. The price sets what you spend. The rate sets what you earn. The return just compares the two.
Example 2: How much face value does Rs 7800 buy in a 6% stock at 130? What is the income?
Step 1. Each Rs 100 of face value costs Rs 130. So face value = 7800 ÷ 130 × 100 = Rs 6000.
Step 2. Income = 6 ÷ 100 × 6000 = Rs 360.
Check. 6000 × 130 ÷ 100 = 7800, which is the money spent.
Why this works. Dividing the money by the price gives the number of Rs 100 blocks. Each block pays the rate.
Example 3: A man wants Rs 450 a year from 9% stock at 120. How much must he invest?
Step 1. Face value needed = 450 ÷ 9 × 100 = Rs 5000.
Step 2. Investment = 120 ÷ 100 × 5000 = Rs 6000.
Check. Income from Rs 5000 at 9% is Rs 450. Cost of Rs 5000 at 120 is Rs 6000.
Why this works. Each Rs 100 of face value pays Rs 9. So Rs 450 needs 50 such blocks.
Example 4: Which is better, a 7% stock at 84 or a 9% stock at 117?
Step 1. First stock: 7 ÷ 84 × 100 = 8.33%.
Step 2. Second stock: 9 ÷ 117 × 100 = 7.69%.
Step 3. Since 8.33 is larger, the 7% stock at 84 is better.
Check. Put Rs 1404 in each. The first gives 1404 ÷ 84 × 7 = Rs 117. The second gives 1404 ÷ 117 × 9 = Rs 108.
Why this works. The same money buys different amounts of stock. The better buy pays more per rupee spent.
Sources: Practice question: comparing two stocks.
Example 5: Rs 6000 of 5% stock is bought at 90, with brokerage of Rs 0.5 per Rs 100. Find the cash needed and the return.
Step 1. Price with brokerage = 90 + 0.5 = Rs 90.5 per Rs 100.
Step 2. Cash needed = 90.5 ÷ 100 × 6000 = Rs 5430.
Step 3. Income = 5 ÷ 100 × 6000 = Rs 300.
Step 4. Return = 300 ÷ 5430 × 100 = 5.52%, to two decimals.
Check. 5430 × 5.52 ÷ 100 is about Rs 300.
Why this works. The fee is part of what you pay. So it raises the cost but not the income.
How do you avoid careless mistakes?
What habits keep answers right?
Write down three numbers first: face value, rate and market price. Then decide which one each step needs.
Ask one question before each step. Is this about income or about cost? Income uses the rate. Cost uses the price.
Check 5
Income from Rs 2000 of 5% stock at 150 is 5 ÷ 150 × 2000.
Check 6
Cost of Rs 2000 of stock at 150 is Rs 3000.
Exam traps
Price trap. The rate always works on face value. Never multiply the rate by the market price.
Premium trap. At 23 premium, the price is 123, not 23.
Brokerage trap. Add brokerage when buying. Subtract it when selling.
Comparison trap. Compare income per rupee spent, not the headline rates.
Rate trap. The return on money spent is not the same as the stock’s rate unless the price is Rs 100.
MCQ on Stocks and Shares
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