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Compiled by: Grace Nganga
Commercial mathematics is essential for professionals working in diverse Kenyan industries such as retail, hospitality, healthcare, agriculture, and finance. Understanding discounts enables accurate pricing, cost control, and profit maximization, which are critical for business sustainability. This chapter focuses on the main types of discounts encountered in commercial transactions: cash discount, trade discount, and quantity discount, with practical calculations applied across various sectors.
Cash discount is an incentive offered by sellers to buyers for prompt payment of invoices within a specified period. It encourages early payment, improving the seller’s cash flow and reducing credit risk. The cash discount is usually expressed as a percentage of the invoice amount and applies only if payment is made within the agreed discount period.
The formula to calculate the cash discount amount is:
$$ \text{Cash Discount} = \frac{\text{Discount Rate}}{100} \times \text{Invoice Amount} $$
The amount payable after applying the cash discount is:
$$ \text{Amount Payable} = \text{Invoice Amount} - \text{Cash Discount} $$
Example 1: A retail shop in Nakuru receives an invoice of Ksh 50,000 with a 5% cash discount if paid within 10 days. Calculate the cash discount and amount payable if payment is made within the discount period.
Given: Invoice Amount = Ksh 50,000, Discount Rate = 5%
$$ \text{Cash Discount} = \frac{5}{100} \times 50,000 $$
$$ = 0.05 \times 50,000 $$
$$ = 2,500 $$
$$ \text{Amount Payable} = 50,000 - 2,500 = 47,500 $$
Answer: Ksh 2,500 cash discount; Ksh 47,500 payable
Example 2: A county hospital receives medical supplies worth Ksh 120,000 with a 3% cash discount for payment within 15 days. Calculate the amount payable after the discount.
Given: Invoice Amount = Ksh 120,000, Discount Rate = 3%
$$ \text{Cash Discount} = \frac{3}{100} \times 120,000 $$
$$ = 0.03 \times 120,000 $$
$$ = 3,600 $$
$$ \text{Amount Payable} = 120,000 - 3,600 = 116,400 $$
Answer: Ksh 3,600 cash discount; Ksh 116,400 payable
Example 3: A cooperative society buys farm equipment worth Ksh 250,000 with a 4.5% cash discount if paid within 7 days. Calculate the cash discount and net payment.
Given: Invoice Amount = Ksh 250,000, Discount Rate = 4.5%
$$ \text{Cash Discount} = \frac{4.5}{100} \times 250,000 $$
$$ = 0.045 \times 250,000 $$
$$ = 11,250 $$
$$ \text{Amount Payable} = 250,000 - 11,250 = 238,750 $$
Answer: Ksh 11,250 cash discount; Ksh 238,750 payable
Example 4: A hotel purchases kitchen appliances worth Ksh 75,000 with a 6% cash discount. The payment is delayed beyond the discount period. Calculate the amount lost due to missing the discount.
Given: Invoice Amount = Ksh 75,000, Discount Rate = 6%
$$ \text{Cash Discount} = \frac{6}{100} \times 75,000 = 4,500 $$
Answer: Ksh 4,500 lost due to late payment
Example 5: A retail business in Kisumu receives an invoice for Ksh 180,000 with a 7% cash discount for payment within 10 days. Calculate the cash discount and amount payable.
Given: Invoice Amount = Ksh 180,000, Discount Rate = 7%
$$ \text{Cash Discount} = \frac{7}{100} \times 180,000 = 12,600 $$
$$ \text{Amount Payable} = 180,000 - 12,600 = 167,400 $$
Answer: Ksh 12,600 cash discount; Ksh 167,400 payable
Example 4 (Expanded): A hotel purchases kitchen appliances worth Ksh 75,000 with a 6% cash discount. The payment is delayed beyond the discount period. Calculate the amount lost due to missing the discount.
Given: Invoice Amount = Ksh 75,000, Discount Rate = 6%
$$ \text{Cash Discount} = \frac{6}{100} \times 75,000 $$$$ = 0.06 \times 75,000 $$$$ = 4,500 $$
Answer: Ksh 4,500 lost due to late payment
A SACCO receives an invoice of Ksh 90,000 with a 5% cash discount if paid within 14 days. Calculate the discount and amount payable if paid on time. (5 marks)
A county government office buys office furniture worth Ksh 150,000 with a 4% cash discount. Find the cash discount amount and net payment. (5 marks)
A retail business has an invoice of Ksh 200,000 with a 6.5% cash discount for payment within 7 days. Calculate the cash discount and amount payable. (6 marks)
A school receives an invoice of Ksh 85,000 with a 3.5% cash discount but pays after the discount period. Calculate the amount lost. (4 marks)
A hotel purchases equipment worth Ksh 320,000 with a 5% cash discount. Calculate the cash discount and amount payable. (6 marks)
Trade discount is a reduction in the list price offered by sellers to buyers, mostly wholesalers or retailers, as an incentive for bulk purchases or business relationships. Unlike cash discount, trade discount is deducted before the invoice is issued and does not depend on payment timing. It is usually expressed as a percentage of the list price.
The formula to calculate the price after trade discount is:
$$ \text{Price After Trade Discount} = \text{List Price} - (\frac{\text{Trade Discount Rate}}{100} \times \text{List Price}) $$
Example 1: A retail store orders goods with a list price of Ksh 60,000 and receives a 10% trade discount. Calculate the amount payable.
Given: List Price = Ksh 60,000, Trade Discount Rate = 10%
$$ \text{Discount Amount} = \frac{10}{100} \times 60,000 = 6,000 $$
$$ \text{Price After Trade Discount} = 60,000 - 6,000 = 54,000 $$
Answer: Ksh 54,000 payable
Example 2: A county hospital orders medical supplies with a list price of Ksh 200,000 and is offered a 15% trade discount. Calculate the discounted price.
Given: List Price = Ksh 200,000, Trade Discount Rate = 15%
$$ \text{Discount Amount} = \frac{15}{100} \times 200,000 = 30,000 $$
$$ \text{Price After Trade Discount} = 200,000 - 30,000 = 170,000 $$
Answer: Ksh 170,000 payable
Example 3: A cooperative buys farming equipment with a list price of Ksh 350,000 and receives a 12% trade discount. Calculate the amount to pay.
Given: List Price = Ksh 350,000, Trade Discount Rate = 12%
$$ \text{Discount Amount} = \frac{12}{100} \times 350,000 = 42,000 $$
$$ \text{Price After Trade Discount} = 350,000 - 42,000 = 308,000 $$
Answer: Ksh 308,000 payable
Example 4: A hotel orders kitchen appliances with a list price of Ksh 80,000 and a trade discount of 8%. Calculate the net price.
Given: List Price = Ksh 80,000, Trade Discount Rate = 8%
$$ \text{Discount Amount} = \frac{8}{100} \times 80,000 = 6,400 $$
$$ \text{Price After Trade Discount} = 80,000 - 6,400 = 73,600 $$
Answer: Ksh 73,600 payable
Example 5: A retail business orders goods with a list price of Ksh 120,000 and receives a 20% trade discount. Calculate the discounted price.
Given: List Price = Ksh 120,000, Trade Discount Rate = 20%
$$ \text{Discount Amount} = \frac{20}{100} \times 120,000 = 24,000 $$
$$ \text{Price After Trade Discount} = 120,000 - 24,000 = 96,000 $$
Answer: Ksh 96,000 payable
A SACCO orders office equipment with a list price of Ksh 75,000 and a 10% trade discount. Calculate the amount to pay. (5 marks)
A county government office buys furniture listed at Ksh 180,000 with a 12% trade discount. Find the discounted price. (5 marks)
A retail shop orders goods worth Ksh 250,000 list price with a 15% trade discount. Calculate the net price. (6 marks)
A cooperative society purchases farming tools with a list price of Ksh 90,000 and receives a 7% trade discount. Calculate the price after discount. (4 marks)
A hotel buys kitchen appliances listed at Ksh 140,000 with a 18% trade discount. Calculate the amount payable. (6 marks)
Quantity discount is a price reduction offered for purchasing goods in large volumes. It encourages bulk buying, reduces handling costs, and improves sales for sellers. The discount can be a fixed percentage applied to the total purchase or tiered based on quantity slabs.
The formula for quantity discount calculation is:
$$ \text{Quantity Discount} = \frac{\text{Discount Rate}}{100} \times \text{Total Purchase Amount} $$
The amount payable after discount is:
$$ \text{Amount Payable} = \text{Total Purchase Amount} - \text{Quantity Discount} $$
Example 1: A retail shop buys 150 units of a product priced at Ksh 500 each. A 5% quantity discount is offered on orders above 100 units. Calculate the total cost after discount.
Given: Unit Price = Ksh 500, Quantity = 150, Discount Rate = 5%
$$ \text{Total Purchase Amount} = 150 \times 500 = 75,000 $$
$$ \text{Quantity Discount} = \frac{5}{100} \times 75,000 = 3,750 $$
$$ \text{Amount Payable} = 75,000 - 3,750 = 71,250 $$
Answer: Ksh 71,250 payable
Example 2: A county hospital orders 300 boxes of medical gloves at Ksh 1,200 each. A 7% quantity discount applies for orders over 250 units. Calculate the amount payable.
Given: Unit Price = Ksh 1,200, Quantity = 300, Discount Rate = 7%
$$ \text{Total Purchase Amount} = 300 \times 1,200 = 360,000 $$
$$ \text{Quantity Discount} = \frac{7}{100} \times 360,000 = 25,200 $$
$$ \text{Amount Payable} = 360,000 - 25,200 = 334,800 $$
Answer: Ksh 334,800 payable
Example 3: A cooperative buys 500 bags of fertilizer at Ksh 2,000 each. A 10% quantity discount applies on orders over 400 bags. Calculate the net amount payable.
Given: Unit Price = Ksh 2,000, Quantity = 500, Discount Rate = 10%
$$ \text{Total Purchase Amount} = 500 \times 2,000 = 1,000,000 $$
$$ \text{Quantity Discount} = \frac{10}{100} \times 1,000,000 = 100,000 $$
$$ \text{Amount Payable} = 1,000,000 - 100,000 = 900,000 $$
Answer: Ksh 900,000 payable
Example 4: A hotel orders 80 mattresses at Ksh 12,000 each. No quantity discount applies for orders below 100 units. Calculate the total cost.
Given: Unit Price = Ksh 12,000, Quantity = 80, Discount Rate = 0%
$$ \text{Total Purchase Amount} = 80 \times 12,000 = 960,000 $$
$$ \text{Quantity Discount} = \frac{0}{100} \times 960,000 = 0 $$
$$ \text{Amount Payable} = 960,000 - 0 = 960,000 $$
Answer: Ksh 960,000 payable
Example 5: A retail business buys 250 units of electronics at Ksh 8,000 each. The supplier offers a 6% discount for orders above 200 units. Calculate the discounted amount and net payment.
Given: Unit Price = Ksh 8,000, Quantity = 250, Discount Rate = 6%
$$ \text{Total Purchase Amount} = 250 \times 8,000 = 2,000,000 $$
$$ \text{Quantity Discount} = \frac{6}{100} \times 2,000,000 = 120,000 $$
$$ \text{Amount Payable} = 2,000,000 - 120,000 = 1,880,000 $$
Answer: Ksh 1,880,000 payable
A SACCO buys 120 chairs at Ksh 3,500 each with a 4% quantity discount for orders above 100 units. Calculate the total cost after discount. (6 marks)
A county government office purchases 400 computers at Ksh 40,000 each with a 5% quantity discount for orders over 300 units. Calculate the amount payable. (7 marks)
A retail business buys 350 units of goods at Ksh 1,500 each with a 7% quantity discount for orders above 300 units. Calculate the net payment. (6 marks)
A cooperative buys 90 bags of maize at Ksh 2,500 each. No discount applies for orders below 100 units. Calculate the total price. (4 marks)
A hotel orders 220 beds at Ksh 18,000 each with an 8% quantity discount for orders above 200 units. Calculate the discounted amount and amount payable. (7 marks)
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Create a free accountThis chapter covered various types of discounts including cash, trade, and quantity discounts, explaining how each affects commercial transactions. It detailed the calculation of commissions as a form of payment based on sales performance. Different methods of calculating wages were discussed, focusing on piece rate and hourly rate systems, followed by practical approaches to computing wages and salaries. The concepts of simple and compound interest were introduced to understand the growth of money over time. Profit margin and mark-ups were explained as key elements in pricing and profitability analysis. The chapter also covered the calculation of gross pay and net pay, highlighting deductions and allowances. Finally, it addressed the depreciation and appreciation of assets, determining hire purchase prices, and managing foreign exchange transactions, providing a comprehensive foundation in commercial mathematics relevant to business and financial operations.
A retail shop in Nakuru offers a trade discount of 12% on an item priced at Ksh 5,000. Calculate the price the customer pays after the discount. (2 marks)
A SACCO agent earns a commission of 4% on all new member shares collected. If the agent collects Ksh 120,000 in shares in a month, find the commission earned. (2 marks)
A retail business in Kisumu offers a cash discount of 5% on purchases paid immediately. If a customer buys goods worth Ksh 12,000 and pays cash, calculate the amount payable after discount. (4 marks)
A county hospital orders medical supplies worth Ksh 150,000 and receives a trade discount of 12%. Find the net amount the hospital will pay. (4 marks)
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