By the end of this chapter, you will be able to:
Mastering these skills will help you handle everyday business calculations confidently and contribute to smooth financial operations in your workplace.
Work-Out Commercial Mathematics is an essential skill for Human Resource professionals in Kenya, particularly when managing payroll, employee benefits, and vendor negotiations. Understanding different types of discounts enables HR practitioners to make informed decisions regarding supplier contracts, staff purchases, and budgeting. This chapter focuses on the three main types of discounts commonly encountered in business transactions: cash discount, trade discount, and quantity discount, with practical calculations relevant to HR operations.
Cash discount is an incentive offered to buyers to encourage early payment of invoices. It helps organizations improve cash flow and reduce outstanding receivables. For HR professionals managing salary advances, staff loans, or supplier payments, calculating cash discounts accurately ensures cost savings and efficient financial management.
The general formula for cash discount is:
$$ \text{Cash Discount} = \text{Invoice Amount} \times \frac{\text{Discount Rate}}{100} $$
Example 1: A retail business buys office supplies worth Ksh 50,000 with a 5% cash discount if paid within 10 days. Calculate the discount amount.
Given: Invoice Amount = Ksh 50,000, Discount Rate = 5%
$$ \text{Cash Discount} = 50,000 \times \frac{5}{100} $$
$$ = 50,000 \times 0.05 $$
$$ = 2,500 $$
Answer: Ksh 2,500
Example 2: A SACCO receives an invoice of Ksh 120,000 for training materials with a 3% cash discount for payment within 15 days. Calculate the amount payable if the discount is taken.
Given: Invoice Amount = Ksh 120,000, Discount Rate = 3%
$$ \text{Cash Discount} = 120,000 \times \frac{3}{100} $$
$$ = 120,000 \times 0.03 $$
$$ = 3,600 $$
Amount payable = Invoice Amount - Cash Discount
$$ = 120,000 - 3,600 $$
$$ = 116,400 $$
Answer: Ksh 116,400
Example 3: A hospital orders medical supplies worth Ksh 75,000 with a 7% cash discount for payment within 7 days. If the payment is delayed and the discount is forfeited, how much extra does the hospital pay?
Given: Invoice Amount = Ksh 75,000, Discount Rate = 7%
$$ \text{Cash Discount} = 75,000 \times \frac{7}{100} $$
$$ = 75,000 \times 0.07 $$
$$ = 5,250 $$
Extra amount paid = Cash Discount forfeited = Ksh 5,250
Answer: Ksh 5,250
Example 4: A county government office has a Ksh 200,000 invoice for office furniture with a 4% cash discount. If the payment is made after the discount period, calculate the percentage increase in payment compared to paying within the discount period.
Given: Invoice Amount = Ksh 200,000, Discount Rate = 4%
Discount amount:
$$ 200,000 \times \frac{4}{100} = 8,000 $$
Amount payable with discount:
$$ 200,000 - 8,000 = 192,000 $$
Percentage increase when paying late:
$$ \frac{200,000 - 192,000}{192,000} \times 100 = \frac{8,000}{192,000} \times 100 $$
$$ = 0.04167 \times 100 = 4.167\% $$
Answer: 4.167% increase
Example 5: A bank purchases software licenses worth Ksh 350,000 with a 6% cash discount if paid within 30 days. Calculate the total payment if the bank pays within the discount period and the savings achieved compared to paying after 30 days.
Given: Invoice Amount = Ksh 350,000, Discount Rate = 6%
Cash Discount:
$$ 350,000 \times \frac{6}{100} = 21,000 $$
Payment within discount period:
$$ 350,000 - 21,000 = 329,000 $$
Savings compared to paying after discount period:
$$ 21,000 $$
Answer: Payment = Ksh 329,000; Savings = Ksh 21,000
A cooperative buys office equipment worth Ksh 90,000 with a 5% cash discount for early payment. Calculate the discount amount. (3 marks)
An NGO receives an invoice of Ksh 150,000 with a 4% cash discount. What is the amount payable if the discount is taken? (4 marks)
A school delays payment on an invoice of Ksh 60,000 with a 3% cash discount. How much extra do they pay? (3 marks)
Calculate the percentage increase in payment if a county government office pays Ksh 250,000 after forfeiting a 5% cash discount. (5 marks)
A bank purchases IT services worth Ksh 400,000 with a 7% cash discount. Find the payment amount if they pay within the discount period. (4 marks)
Trade discount is a reduction offered by sellers to buyers, usually based on the buyer’s status or the nature of the trade. It is common in bulk purchasing or between businesses and is deducted from the list price before any other charges or taxes. HR professionals negotiating contracts for employee welfare supplies or bulk staff uniforms use trade discount calculations to optimize procurement costs.
The formula for trade discount is:
$$ \text{Trade Discount} = \text{List Price} \times \frac{\text{Trade Discount Rate}}{100} $$
Net price after trade discount:
$$ \text{Net Price} = \text{List Price} - \text{Trade Discount} $$
Example 1: A hotel orders uniforms listed at Ksh 80,000 with a 10% trade discount. Calculate the discount and net price.
Given: List Price = Ksh 80,000, Trade Discount Rate = 10%
$$ \text{Trade Discount} = 80,000 \times \frac{10}{100} $$
$$ = 80,000 \times 0.10 $$
$$ = 8,000 $$
Net Price:
$$ 80,000 - 8,000 = 72,000 $$
Answer: Discount = Ksh 8,000; Net Price = Ksh 72,000
Example 2: A retail business buys office furniture with a list price of Ksh 150,000 and a trade discount of 15%. Find the trade discount and net price.
Given: List Price = Ksh 150,000, Trade Discount Rate = 15%
$$ \text{Trade Discount} = 150,000 \times \frac{15}{100} $$
$$ = 150,000 \times 0.15 $$
$$ = 22,500 $$
Net Price:
$$ 150,000 - 22,500 = 127,500 $$
Answer: Discount = Ksh 22,500; Net Price = Ksh 127,500
Example 3: A cooperative purchases agricultural tools with a list price of Ksh 95,000 and a trade discount of 12%. Calculate the net price.
Given: List Price = Ksh 95,000, Trade Discount Rate = 12%
$$ \text{Trade Discount} = 95,000 \times \frac{12}{100} $$
$$ = 11,400 $$
Net Price:
$$ 95,000 - 11,400 = 83,600 $$
Answer: Net Price = Ksh 83,600
Example 4: A county government office orders office chairs listed at Ksh 200,000 with a 20% trade discount. Calculate the amount payable.
Given: List Price = Ksh 200,000, Trade Discount Rate = 20%
$$ \text{Trade Discount} = 200,000 \times \frac{20}{100} $$
$$ = 40,000 $$
Net Price:
$$ 200,000 - 40,000 = 160,000 $$
Answer: Amount Payable = Ksh 160,000
Example 5: A hospital orders medical equipment with a list price of Ksh 500,000 and receives a 25% trade discount. Calculate the trade discount and net price.
Given: List Price = Ksh 500,000, Trade Discount Rate = 25%
$$ \text{Trade Discount} = 500,000 \times \frac{25}{100} $$
$$ = 125,000 $$
Net Price:
$$ 500,000 - 125,000 = 375,000 $$
Answer: Discount = Ksh 125,000; Net Price = Ksh 375,000
Calculate the trade discount and net price for a list price of Ksh 100,000 with a 12% trade discount. (4 marks)
A SACCO buys computers listed at Ksh 180,000 with a 15% trade discount. Find the net price. (4 marks)
A school orders textbooks with a list price of Ksh 250,000 and a trade discount of 18%. Find the discount and net price. (5 marks)
A bank receives office supplies with a list price of Ksh 130,000 and a trade discount of 10%. Calculate the amount payable. (4 marks)
Calculate the net price for a list price of Ksh 400,000 with a 22% trade discount. (4 marks)
Quantity discount is offered when buyers purchase goods in large volumes, encouraging bulk buying and reducing per unit cost. HR departments managing staff welfare purchases or procurement of training materials leverage quantity discounts to maximize budget efficiency. Calculating quantity discounts helps in planning bulk orders and negotiating better deals.
The formula for quantity discount is:
$$ \text{Quantity Discount} = \text{Unit Price} \times \text{Quantity} \times \frac{\text{Discount Rate}}{100} $$
Net price after discount:
$$ \text{Net Price} = (\text{Unit Price} \times \text{Quantity}) - \text{Quantity Discount} $$
Example 1: A school orders 500 textbooks priced at Ksh 800 each with a 5% quantity discount. Calculate the discount and total cost.
Given: Unit Price = Ksh 800, Quantity = 500, Discount Rate = 5%
$$ \text{Quantity Discount} = 800 \times 500 \times \frac{5}{100} $$
$$ = 400,000 \times 0.05 $$
$$ = 20,000 $$
Total cost:
$$ 400,000 - 20,000 = 380,000 $$
Answer: Discount = Ksh 20,000; Total Cost = Ksh 380,000
Example 2: A county government orders 1,200 chairs at Ksh 1,500 each with a 10% quantity discount. Calculate the total discount and net price.
Given: Unit Price = Ksh 1,500, Quantity = 1,200, Discount Rate = 10%
$$ \text{Quantity Discount} = 1,500 \times 1,200 \times \frac{10}{100} $$
$$ = 1,800,000 \times 0.10 $$
$$ = 180,000 $$
Net price:
$$ 1,800,000 - 180,000 = 1,620,000 $$
Answer: Discount = Ksh 180,000; Net Price = Ksh 1,620,000
Example 3: A hospital purchases 300 units of medical gloves at Ksh 450 each with a 7% quantity discount. Calculate the discount and total amount payable.
Given: Unit Price = Ksh 450, Quantity = 300, Discount Rate = 7%
$$ \text{Quantity Discount} = 450 \times 300 \times \frac{7}{100} $$
$$ = 135,000 \times 0.07 $$
$$ = 9,450 $$
Total payable:
$$ 135,000 - 9,450 = 125,550 $$
Answer: Discount = Ksh 9,450; Total Payable = Ksh 125,550
Example 4: A cooperative buys 2,000 units of fertilizer at Ksh 1,200 each with a 12% quantity discount. Calculate the quantity discount and net price.
Given: Unit Price = Ksh 1,200, Quantity = 2,000, Discount Rate = 12%
$$ \text{Quantity Discount} = 1,200 \times 2,000 \times \frac{12}{100} $$
$$ = 2,400,000 \times 0.12 $$
$$ = 288,000 $$
Net price:
$$ 2,400,000 - 288,000 = 2,112,000 $$
Answer: Discount = Ksh 288,000; Net Price = Ksh 2,112,000
Example 5: A bank orders 750 laptops at Ksh 80,000 each with a 15% quantity discount. Calculate the total discount and amount payable.
Given: Unit Price = Ksh 80,000, Quantity = 750, Discount Rate = 15%
$$ \text{Quantity Discount} = 80,000 \times 750 \times \frac{15}{100} $$
$$ = 60,000,000 \times 0.15 $$
$$ = 9,000,000 $$
Amount payable:
$$ 60,000,000 - 9,000,000 = 51,000,000 $$
Answer: Discount = Ksh 9,000,000; Amount Payable = Ksh 51,000,000
Calculate the quantity discount and total price for 600 units priced at Ksh 900 each with a 6% discount. (5 marks)
A county government orders 1,000 laptops at Ksh 50,000 each with a 10% quantity discount. Find the discount and net price. (5 marks)
A hospital buys 400 units of medical equipment at Ksh 1,200 each with an 8% quantity discount. Calculate the total discount and amount payable. (5 marks)
A cooperative orders 1,500 bags of maize at Ksh 2,000 each with a 7% quantity discount. Find the total cost after discount. (5 marks)
Calculate the quantity discount and net price for 900 office chairs at Ksh 3,500 each with a 12% discount. (5 marks)
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Create a free accountThis chapter covered essential commercial mathematics concepts starting with the different types of discounts, including cash, trade, and quantity discounts, explaining how each affects pricing. It then explored commissions, detailing how they are calculated as a percentage of sales or transactions. Various methods of calculating wages were discussed, focusing on piece rate and hourly rate systems, followed by practical computations of wages and salaries. The chapter also introduced the basics of simple and compound interest, demonstrating how to find principal, rate, and time using relevant formulas. Understanding profit margin and mark-ups was emphasized to assess business profitability accurately. Calculations of gross pay and net pay were explained to highlight deductions and earnings. Finally, the chapter addressed depreciation and appreciation of assets, determining hire purchase prices, and computing foreign exchange transactions, all critical for sound financial decision-making in business contexts.
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 receives a trade discount of 10% and a quantity discount of 5% on an order worth Ksh 250,000. Calculate the net amount payable after both discounts. (3 marks)
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