By the end of this chapter, you will be able to:
These skills will help you handle everyday business calculations confidently and contribute effectively to your workplace’s financial success.
Commercial mathematics is essential for accountancy professionals in Kenya as it underpins daily business transactions involving buying and selling. Mastery of discounts, profit and loss calculations, margins, and mark-ups is critical for accurate financial analysis and decision-making in enterprises ranging from retail shops to cooperatives. This chapter develops practical skills to compute these values, enabling professionals to assess business performance and pricing strategies effectively.
Commercial transactions often involve adjustments such as discounts and mark-ups that affect the final selling price and profitability. Understanding how to calculate these accurately ensures transparent pricing, competitive advantage, and compliance with accounting standards in Kenyan businesses.
Discounts reduce the price payable by a buyer and are commonly used to encourage prompt payment or bulk purchases. The main types of discounts are trade discount and cash discount.
The general formula for calculating discount amount is:
$$\text{Discount} = \text{List Price} \times \frac{\text{Discount Rate}}{100}$$
The amount payable after discount is:
$$\text{Price after Discount} = \text{List Price} - \text{Discount}$$
Example 1: A retail store offers a trade discount of 10% on goods priced at Ksh 5,000. Find the price payable.
Given: List Price = Ksh 5,000, Discount Rate = 10%
$$\text{Discount} = 5000 \times \frac{10}{100}$$
$$= 5000 \times 0.10$$
$$= 500 \text{ Ksh}$$
$$\text{Price after Discount} = 5000 - 500$$
$$= 4500 \text{ Ksh}$$
Answer: Ksh 4,500
Example 2: A supplier gives a cash discount of 5% on an invoice amount of Ksh 12,000 if paid within 10 days. Calculate the discount and the amount to be paid if paid within the discount period.
Given: Invoice Amount = Ksh 12,000, Cash Discount Rate = 5%
$$\text{Discount} = 12000 \times \frac{5}{100}$$
$$= 12000 \times 0.05$$
$$= 600 \text{ Ksh}$$
$$\text{Amount Payable} = 12000 - 600$$
$$= 11400 \text{ Ksh}$$
Answer: Discount = Ksh 600; Amount payable = Ksh 11,400
Example 3: A wholesaler sells goods at Ksh 20,000 with a trade discount of 15% followed by a cash discount of 3%. Calculate the final amount payable if both discounts apply successively.
Given: List Price = Ksh 20,000, Trade Discount = 15%, Cash Discount = 3%
Step 1: Calculate price after trade discount
$$\text{Price after Trade Discount} = 20000 - (20000 \times \frac{15}{100})$$
$$= 20000 - 3000$$
$$= 17000 \text{ Ksh}$$
Step 2: Calculate cash discount on Ksh 17,000
$$\text{Cash Discount} = 17000 \times \frac{3}{100}$$
$$= 17000 \times 0.03$$
$$= 510 \text{ Ksh}$$
Step 3: Final price after cash discount
$$\text{Final Price} = 17000 - 510$$
$$= 16490 \text{ Ksh}$$
Answer: Ksh 16,490
Profit or loss arises when goods are sold for more or less than their cost price. Calculating profit or loss is essential for assessing business viability.
Formulas:
$$\text{Profit} = \text{Selling Price} - \text{Cost Price}$$
$$\text{Loss} = \text{Cost Price} - \text{Selling Price}$$
Profit or loss percentage is calculated as:
$$\text{Profit \%} = \frac{\text{Profit}}{\text{Cost Price}} \times 100$$
$$\text{Loss \%} = \frac{\text{Loss}}{\text{Cost Price}} \times 100$$
Example 1: A trader buys goods for Ksh 8,000 and sells them for Ksh 9,200. Calculate the profit and profit percentage.
Given: Cost Price = Ksh 8,000, Selling Price = Ksh 9,200
$$\text{Profit} = 9200 - 8000$$
$$= 1200 \text{ Ksh}$$
$$\text{Profit \%} = \frac{1200}{8000} \times 100$$
$$= 15\%$$
Answer: Profit = Ksh 1,200; Profit percentage = 15%
Example 2: A shopkeeper sells an item for Ksh 7,500 at a loss of 10%. Find the cost price.
Given: Selling Price = Ksh 7,500, Loss \% = 10%
Using loss percentage formula:
$$\text{Loss} = \frac{10}{100} \times \text{Cost Price} = 0.10 \times \text{Cost Price}$$
Since
$$\text{Selling Price} = \text{Cost Price} - \text{Loss} = \text{Cost Price} - 0.10 \times \text{Cost Price} = 0.90 \times \text{Cost Price}$$
Then,
$$7500 = 0.90 \times \text{Cost Price}$$
$$\text{Cost Price} = \frac{7500}{0.90}$$
$$= 8333.33 \text{ Ksh}$$
Answer: Cost Price = Ksh 8,333.33
Example 3: A cooperative buys maize at Ksh 1,200 per bag and sells it at a 12.5% profit. What is the selling price?
Given: Cost Price = Ksh 1,200, Profit \% = 12.5%
$$\text{Profit} = \frac{12.5}{100} \times 1200$$
$$= 0.125 \times 1200$$
$$= 150 \text{ Ksh}$$
$$\text{Selling Price} = 1200 + 150$$
$$= 1350 \text{ Ksh}$$
Answer: Selling Price = Ksh 1,350
Margin represents the gross profit expressed as a percentage of the selling price. It is useful for pricing strategies and profitability analysis.
Formula:
$$\text{Margin \%} = \frac{\text{Profit}}{\text{Selling Price}} \times 100$$
Alternatively,
$$\text{Margin \%} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Selling Price}} \times 100$$
Example 1: A retailer sells goods for Ksh 10,000 which cost Ksh 8,000. Calculate the margin percentage.
Given: Selling Price = Ksh 10,000, Cost Price = Ksh 8,000
$$\text{Profit} = 10000 - 8000 = 2000 \text{ Ksh}$$
$$\text{Margin \%} = \frac{2000}{10000} \times 100$$
$$= 20\%$$
Answer: Margin = 20%
Example 2: If the margin on a product is 25% and the selling price is Ksh 12,000, find the cost price.
Given: Margin \% = 25%, Selling Price = Ksh 12,000
Using margin formula:
$$25 = \frac{SP - CP}{SP} \times 100$$
$$\frac{SP - CP}{SP} = \frac{25}{100} = 0.25$$
$$SP - CP = 0.25 \times SP$$
$$CP = SP - 0.25 \times SP = 0.75 \times SP$$
$$CP = 0.75 \times 12000$$
$$= 9000 \text{ Ksh}$$
Answer: Cost Price = Ksh 9,000
Example 3: A wholesaler sells an item at Ksh 15,000 with a margin of 30%. What is the cost price and profit?
Given: Selling Price = Ksh 15,000, Margin \% = 30%
$$\text{Cost Price} = SP \times (1 - \frac{Margin \%}{100})$$
$$= 15000 \times (1 - 0.30)$$
$$= 15000 \times 0.70$$
$$= 10500 \text{ Ksh}$$
$$\text{Profit} = SP - CP = 15000 - 10500 = 4500 \text{ Ksh}$$
Answer: Cost Price = Ksh 10,500; Profit = Ksh 4,500
Mark-up is the amount added to the cost price to determine the selling price. It is expressed as a percentage of the cost price and is essential for setting prices that cover costs and desired profit.
Formula:
$$\text{Mark-up \%} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100$$
Or equivalently,
$$\text{Selling Price} = \text{Cost Price} + \text{Mark-up Amount}$$
Example 1: A retailer buys a product at Ksh 4,000 and applies a mark-up of 25%. Find the selling price.
Given: Cost Price = Ksh 4,000, Mark-up \% = 25%
$$\text{Mark-up Amount} = 4000 \times \frac{25}{100}$$
$$= 4000 \times 0.25$$
$$= 1000 \text{ Ksh}$$
$$\text{Selling Price} = 4000 + 1000$$
$$= 5000 \text{ Ksh}$$
Answer: Selling Price = Ksh 5,000
Example 2: A business wants a mark-up of 40% on cost price. If the selling price is Ksh 14,000, find the cost price.
Given: Mark-up \% = 40%, Selling Price = Ksh 14,000
Using formula:
$$SP = CP + (Mark-up \% \times CP) = CP \times (1 + \frac{Mark-up \%}{100})$$
$$14000 = CP \times (1 + 0.40) = CP \times 1.40$$
$$CP = \frac{14000}{1.40}$$
$$= 10000 \text{ Ksh}$$
Answer: Cost Price = Ksh 10,000
Example 3: An item costs Ksh 18,000 and is marked up by 50%. Later, the item is sold at a 10% discount on the marked price. Calculate the final selling price.
Given: Cost Price = Ksh 18,000, Mark-up \% = 50%, Discount \% = 10%
Step 1: Calculate marked price
$$\text{Marked Price} = 18000 + (18000 \times \frac{50}{100})$$
$$= 18000 + 9000$$
$$= 27000 \text{ Ksh}$$
Step 2: Calculate discount amount
$$\text{Discount} = 27000 \times \frac{10}{100}$$
$$= 2700 \text{ Ksh}$$
Step 3: Calculate final selling price
$$\text{Selling Price} = 27000 - 2700$$
$$= 24300 \text{ Ksh}$$
Answer: Final Selling Price = Ksh 24,300
A supermarket offers a trade discount of 12% on goods priced at Ksh 8,500. Calculate the price after discount. (5 marks)
A trader sells a product at Ksh 15,000 and makes a profit of 20%. Find the cost price. (5 marks)
Calculate the margin percentage if the cost price of an item is Ksh 6,000 and the selling price is Ksh 7,500. (5 marks)
A retailer applies a mark-up of 35% on the cost price of Ksh 9,000. Calculate the selling price. (5 marks)
An item is marked up by 40% on cost price and then sold at a 5% discount on the marked price. If the cost price is Ksh 12,000, find the final selling price. (10 marks)
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Create a free accountThis chapter covers essential commercial mathematics concepts used in everyday business transactions. It begins with buying and selling calculations, focusing on discounts, profit and loss, margins, and mark-ups to determine selling prices and profitability. The chapter then explains commissions and salaries, including piece and hourly rates, gross and net pay, and the calculation of PAYE deductions. It proceeds to bills calculations, demonstrating how to compute charges for water and electricity consumption. Interest calculations are addressed next, distinguishing between simple and compound interest and their applications in finance. The chapter also explores asset valuation through depreciation and appreciation methods to assess changes in value over time. Hire purchase agreements are examined, highlighting payment structures and interest implications. Lastly, foreign currency exchange transactions are explained to facilitate international trade and currency conversions in business.
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