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Compiled by: John Gitau
Work-out commercial mathematics is essential for human resource professionals in Kenya who often manage procurement, budgeting, and payroll activities requiring precise discount calculations. Understanding different types of discounts helps HR specialists negotiate better deals with suppliers, optimize costs, and accurately compute net payables and receivables. This chapter focuses on the three main discount types encountered in business transactions: cash discount, trade discount, and quantity discount, with practical worked examples relevant to HR operations.
Cash discount is an incentive offered to buyers for prompt payment of invoices, usually within a specified short period. This discount helps organizations improve cash flow and reduce credit risk by encouraging early payments. The formula to calculate the cash discount amount is:
$$ \text{Cash Discount} = \text{Invoice Amount} \times \frac{\text{Discount Rate}}{100} $$
Example 1:
A county government office receives an invoice of Ksh 50,000 with a 5% cash discount if paid within 10 days. Calculate the cash discount and the amount payable if paid within the discount period.
Given: Invoice Amount = Ksh 50,000, Discount Rate = 5%
$$ \text{Cash Discount} = 50,000 \times \frac{5}{100} $$$$ = 50,000 \times 0.05 $$$$ = 2,500 \text{ Ksh} $$
Answer: Ksh 2,500
Amount payable = Invoice Amount - Cash Discount$$ = 50,000 - 2,500 = 47,500 \text{ Ksh} $$
Example 2:
A cooperative receives goods worth Ksh 120,000 with a 3% cash discount if payment is made within 15 days. Find the cash discount and net payment.
Given: Invoice Amount = Ksh 120,000, Discount Rate = 3%
$$ \text{Cash Discount} = 120,000 \times \frac{3}{100} $$$$ = 120,000 \times 0.03 $$$$ = 3,600 \text{ Ksh} $$
Answer: Ksh 3,600
Net payment =$$ 120,000 - 3,600 = 116,400 \text{ Ksh} $$
Example 3:
A retail business is invoiced Ksh 75,000 with a 7% cash discount valid for 5 days. Calculate the cash discount and payment amount.
Given: Invoice Amount = Ksh 75,000, Discount Rate = 7%
$$ \text{Cash Discount} = 75,000 \times \frac{7}{100} $$$$ = 75,000 \times 0.07 $$$$ = 5,250 \text{ Ksh} $$
Answer: Ksh 5,250
Net amount payable =$$ 75,000 - 5,250 = 69,750 \text{ Ksh} $$
Example 4:
A hotel is billed Ksh 200,000 with a 4% cash discount if paid within 10 days. Calculate the cash discount and total payment.
Given: Invoice Amount = Ksh 200,000, Discount Rate = 4%
$$ \text{Cash Discount} = 200,000 \times \frac{4}{100} $$$$ = 200,000 \times 0.04 $$$$ = 8,000 \text{ Ksh} $$
Answer: Ksh 8,000
Payment =$$ 200,000 - 8,000 = 192,000 \text{ Ksh} $$
Example 5:
A SACCO receives an invoice of Ksh 350,000 with a 2.5% cash discount for payment within 7 days. Find the discount and payable amount.
Given: Invoice Amount = Ksh 350,000, Discount Rate = 2.5%
$$ \text{Cash Discount} = 350,000 \times \frac{2.5}{100} $$$$ = 350,000 \times 0.025 $$$$ = 8,750 \text{ Ksh} $$
Answer: Ksh 8,750
Net payment =$$ 350,000 - 8,750 = 341,250 \text{ Ksh} $$
Example 6:
A farmer was allowed a cash discount of Ksh 175 on farm implements worth Ksh 3,500. What was the percentage discount?
Given: Discount = 175 Ksh, Invoice Amount = 3,500 Ksh
Formula:$$ \text{Discount Rate} = \frac{\text{Cash Discount}}{\text{Invoice Amount}} \times 100 $$ Substitution:$$ \text{Discount Rate} = \frac{175}{3,500} \times 100 = 0.05 \times 100 = 5\% $$ Answer: 5\%
Example 7:
Jane paid Ksh 12,000 for a TV set after she was allowed a discount of 16\%. What was the marked price of the TV?
Given: Selling Price = 12,000 Ksh, Discount Rate = 16\%
Let Marked Price = M
Discount = M \times \frac{16}{100}
Selling Price = M - Discount = M - M \times \frac{16}{100} = M \times (1 - 0.16) = M \times 0.84
So,$$ 12,000 = M \times 0.84 $$$$ M = \frac{12,000}{0.84} = 14,285.71 \text{ Ksh} $$ Answer: Ksh 14,285.71
Trade discount is a reduction in the list price granted by suppliers to buyers, usually based on the business relationship or industry norms. It is deducted before any cash discount or taxes are applied and is not recorded in accounting books as a separate entry. The formula for trade discount is:
$$ \text{Trade Discount} = \text{List Price} \times \frac{\text{Trade Discount Rate}}{100} $$
Example 1:
A bank orders office supplies priced at Ksh 40,000 with a 10% trade discount. Calculate the trade discount and the price after discount.
Given: List Price = Ksh 40,000, Trade Discount Rate = 10%
$$ \text{Trade Discount} = 40,000 \times \frac{10}{100} $$$$ = 40,000 \times 0.10 $$$$ = 4,000 \text{ Ksh} $$
Answer: Ksh 4,000
Price after discount =$$ 40,000 - 4,000 = 36,000 \text{ Ksh} $$
Example 2:
A school orders textbooks costing Ksh 150,000 with a trade discount of 15%. Find the trade discount and net price.
Given: List Price = Ksh 150,000, Trade Discount Rate = 15%
$$ \text{Trade Discount} = 150,000 \times \frac{15}{100} $$$$ = 150,000 \times 0.15 $$$$ = 22,500 \text{ Ksh} $$
Answer: Ksh 22,500
Net price =$$ 150,000 - 22,500 = 127,500 \text{ Ksh} $$
Example 3:
A hotel buys furniture listed at Ksh 320,000 with a 12% trade discount. Calculate the discount and payable amount.
Given: List Price = Ksh 320,000, Trade Discount Rate = 12%
$$ \text{Trade Discount} = 320,000 \times \frac{12}{100} $$$$ = 320,000 \times 0.12 $$$$ = 38,400 \text{ Ksh} $$
Answer: Ksh 38,400
Payable price =$$ 320,000 - 38,400 = 281,600 \text{ Ksh} $$
Example 4:
A county government office orders computer equipment worth Ksh 600,000 with a 5% trade discount. Calculate the trade discount and discounted price.
Given: List Price = Ksh 600,000, Trade Discount Rate = 5%
$$ \text{Trade Discount} = 600,000 \times \frac{5}{100} $$$$ = 600,000 \times 0.05 $$$$ = 30,000 \text{ Ksh} $$
Answer: Ksh 30,000
Discounted price =$$ 600,000 - 30,000 = 570,000 \text{ Ksh} $$
Example 5:
A cooperative purchases farm inputs listed at Ksh 220,000 with a 20% trade discount. Find the trade discount and net price.
Given: List Price = Ksh 220,000, Trade Discount Rate = 20%
$$ \text{Trade Discount} = 220,000 \times \frac{20}{100} $$$$ = 220,000 \times 0.20 $$$$ = 44,000 \text{ Ksh} $$
Answer: Ksh 44,000
Net price =$$ 220,000 - 44,000 = 176,000 \text{ Ksh} $$
Example 6:
A school bought textbooks worth Ksh 27,027 from a bookseller. If the bookseller allowed a discount of 10\%, what was the cost of the books without the discount?
Given: Net Price (after discount) = Ksh 27,027, Discount Rate = 10\%
Let Marked Price = M
Discount = M \times \frac{10}{100}
Net Price = M - Discount = M - M \times 0.10 = M \times 0.90
So,$$ 27,027 = M \times 0.90 $$$$ M = \frac{27,027}{0.90} = 30,030 \text{ Ksh} $$ Answer: Ksh 30,030
Example 7:
Calculate the marked price on a bag of cement selling at Ksh 570 after a discount of 5\% is offered.
Given: Selling Price = Ksh 570, Discount Rate = 5\%
Let Marked Price = M
Selling Price = M - M \times 0.05 = M \times 0.95
So,$$ 570 = M \times 0.95 $$$$ M = \frac{570}{0.95} = 600 \text{ Ksh} $$ Answer: Ksh 600
Example 8:
An umbrella and a pen are sold at a discount of 8\% and 3\% respectively. Calculate the overall discount offered on the two commodities, if the cost of the umbrella is four times that of the pen.
Let cost of pen = x Ksh, umbrella = 4x Ksh
Total cost = x + 4x = 5x Ksh
Discount on umbrella = 4x \times \frac{8}{100} = 0.32x
Discount on pen = x \times \frac{3}{100} = 0.03x
Total discount = 0.32x + 0.03x = 0.35x
Overall discount rate:$$ \text{Overall Discount Rate} = \frac{0.35x}{5x} \times 100 = \frac{0.35}{5} \times 100 = 0.07 \times 100 = 7\% $$ Answer: 7\% overall discount
Quantity discount is a price reduction offered to buyers who purchase goods in large volumes. This discount encourages bulk buying, reduces handling costs, and strengthens supplier-buyer relationships. The quantity discount is applied on the total price of the goods purchased. The formula is:
$$ \text{Quantity Discount} = \text{Total Price} \times \frac{\text{Quantity Discount Rate}}{100} $$
Example 1:
A retail business buys 500 units of stationery at Ksh 200 per unit with a 5% quantity discount. Calculate the total price before discount, discount amount, and net payment.
Given: Unit Price = Ksh 200, Quantity = 500, Discount Rate = 5%
Total price before discount:$$ 200 \times 500 = 100,000 \text{ Ksh} $$
Quantity discount:$$ 100,000 \times \frac{5}{100} = 100,000 \times 0.05 = 5,000 \text{ Ksh} $$
Net payment:$$ 100,000 - 5,000 = 95,000 \text{ Ksh} $$
Answer: Ksh 95,000
Example 2:
A school orders 1,200 textbooks at Ksh 350 each with a 7% quantity discount. Find the total price, discount, and amount payable.
Given: Unit Price = Ksh 350, Quantity = 1,200, Discount Rate = 7%
Total price:$$ 350 \times 1,200 = 420,000 \text{ Ksh} $$
Quantity discount:$$ 420,000 \times \frac{7}{100} = 420,000 \times 0.07 = 29,400 \text{ Ksh} $$
Net payment:$$ 420,000 - 29,400 = 390,600 \text{ Ksh} $$
Answer: Ksh 390,600
Example 3:
A cooperative purchases 2,000 bags of fertilizer at Ksh 1,000 per bag with a 10% quantity discount. Calculate the total cost, discount, and payable amount.
Given: Unit Price = Ksh 1,000, Quantity = 2,000, Discount Rate = 10%
Total price:$$ 1,000 \times 2,000 = 2,000,000 \text{ Ksh} $$
Quantity discount:$$ 2,000,000 \times \frac{10}{100} = 2,000,000 \times 0.10 = 200,000 \text{ Ksh} $$
Net payment:$$ 2,000,000 - 200,000 = 1,800,000 \text{ Ksh} $$
Answer: Ksh 1,800,000
Example 4:
A hotel buys 300 mattresses priced at Ksh 12,000 each with a 6% quantity discount. Find the total price, discount, and net payment.
Given: Unit Price = Ksh 12,000, Quantity = 300, Discount Rate = 6%
Total price:$$ 12,000 \times 300 = 3,600,000 \text{ Ksh} $$
Quantity discount:$$ 3,600,000 \times \frac{6}{100} = 3,600,000 \times 0.06 = 216,000 \text{ Ksh} $$
Net payment:$$ 3,600,000 - 216,000 = 3,384,000 \text{ Ksh} $$
Answer: Ksh 3,384,000
Example 5:
A county government orders 150 vehicles at Ksh 3,500,000 each with an 8% quantity discount. Calculate the total cost, discount, and amount payable.
Given: Unit Price = Ksh 3,500,000, Quantity = 150, Discount Rate = 8%
Total price:$$ 3,500,000 \times 150 = 525,000,000 \text{ Ksh} $$
Quantity discount:$$ 525,000,000 \times \frac{8}{100} = 525,000,000 \times 0.08 = 42,000,000 \text{ Ksh} $$
Net payment:$$ 525,000,000 - 42,000,000 = 483,000,000 \text{ Ksh} $$
Answer: Ksh 483,000,000
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Create a free accountThis chapter covered essential aspects of commercial mathematics starting with different types of discounts including cash, trade, and quantity discounts, explaining how each reduces the selling price under specific conditions. It then explored commissions as a form of earnings based on sales performance. Various methods of calculating wages were examined, focusing on piece rate and hourly rate systems, followed by practical approaches to computing wages and salaries. The fundamentals of simple and compound interest were introduced, detailing how to find principal, rate, and time using relevant formulas. Profit margin and mark-ups were analyzed to understand business profitability and pricing strategies. The chapter also explained the calculation of gross pay and net pay, highlighting deductions and allowances. Additionally, concepts of depreciation and appreciation of assets were discussed to evaluate asset value changes over time. Finally, methods for determining hire purchase prices and computing foreign exchange transactions were presented, emphasizing their significance in financial dealings.
A supplier offers a cash discount of 5% on an invoice amount of Ksh 120,000 if payment is made within 10 days. Calculate the amount payable after the discount. (2 marks)
A company orders goods worth Ksh 250,000 and is entitled to a trade discount of 12%. Calculate the net amount payable after the trade discount. (2 marks)
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