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Work-out commercial mathematics is essential for banking and finance professionals in Kenya who regularly handle transactions involving discounts. Understanding how to compute various discounts accurately impacts pricing, profitability, and customer relations in financial institutions, retail banking, and corporate finance departments. This chapter focuses on three common types of commercial discounts: cash discount, trade discount, and quantity discount, providing practical computational techniques relevant to Kenyan financial contexts.
Commercial discounts are reductions offered by sellers to buyers to encourage prompt payment, bulk purchases, or to build long-term business relationships. Each type of discount has a specific calculation method and financial implication that banking and finance professionals must master for accurate financial analysis and reporting.
Cash discounts are deductions allowed to buyers for early payment of invoices, promoting liquidity and reducing credit risk for sellers. The cash discount is typically expressed as a percentage of the invoice amount and applies if payment is made within a specified period.
The formula for calculating the cash discount amount is:
$$ \text{Cash Discount} = \text{Invoice Amount} \times \frac{\text{Discount Rate}}{100} $$
The amount payable after discount is:
$$ \text{Amount Payable} = \text{Invoice Amount} - \text{Cash Discount} $$
Example 1: A retail business receives an invoice of Ksh 50,000 with a 5% cash discount if paid within 10 days. Calculate the discount and amount payable.
Given: Invoice Amount = Ksh 50,000, Discount Rate = 5%
$$ \text{Cash Discount} = 50,000 \times \frac{5}{100} $$$$ = 50,000 \times 0.05 $$$$ = 2,500 $$
$$ \text{Amount Payable} = 50,000 - 2,500 = 47,500 $$
Answer: Cash Discount = Ksh 2,500, Amount Payable = Ksh 47,500
Example 2: A SACCO has an outstanding invoice of Ksh 120,000 with a 3% cash discount for payment within 7 days. What is the amount payable if the discount is claimed?
Given: Invoice Amount = Ksh 120,000, Discount Rate = 3%
$$ \text{Cash Discount} = 120,000 \times \frac{3}{100} $$$$ = 120,000 \times 0.03 $$$$ = 3,600 $$
$$ \text{Amount Payable} = 120,000 - 3,600 = 116,400 $$
Answer: Cash Discount = Ksh 3,600, Amount Payable = Ksh 116,400
Example 3: A hotel receives an invoice of Ksh 75,000 with a 4% cash discount for payment within 15 days. If the hotel pays after 15 days, what is the loss in discount?
Given: Invoice Amount = Ksh 75,000, Discount Rate = 4%
$$ \text{Cash Discount} = 75,000 \times \frac{4}{100} $$$$ = 75,000 \times 0.04 $$$$ = 3,000 $$
Answer: Loss in discount = Ksh 3,000
Example 4: A bank is offered a 6% cash discount on a Ksh 200,000 invoice if paid within 5 days. Calculate the amount payable if the discount is claimed.
Given: Invoice Amount = Ksh 200,000, Discount Rate = 6%
$$ \text{Cash Discount} = 200,000 \times \frac{6}{100} $$$$ = 200,000 \times 0.06 $$$$ = 12,000 $$
$$ \text{Amount Payable} = 200,000 - 12,000 = 188,000 $$
Answer: Cash Discount = Ksh 12,000, Amount Payable = Ksh 188,000
Example 5: A cooperative society has an invoice of Ksh 350,000 with a 2.5% cash discount. Calculate the amount payable after discount.
Given: Invoice Amount = Ksh 350,000, Discount Rate = 2.5%
$$ \text{Cash Discount} = 350,000 \times \frac{2.5}{100} $$$$ = 350,000 \times 0.025 $$$$ = 8,750 $$
$$ \text{Amount Payable} = 350,000 - 8,750 = 341,250 $$
Answer: Cash Discount = Ksh 8,750, Amount Payable = Ksh 341,250
Trade discounts are deductions offered by sellers to buyers on the list price of goods, usually to intermediaries or bulk buyers, without altering the invoice price or payment terms. Trade discounts are not recorded in financial accounts but are essential for calculating net prices.
The formula for calculating the net price after trade discount is:
$$ \text{Net Price} = \text{List Price} \times (1 - \frac{\text{Trade Discount Rate}}{100}) $$
For multiple trade discounts applied successively, the net price is calculated by applying each discount one after another.
Example 1: A bank buys office equipment with a list price of Ksh 80,000 and is offered a 10% trade discount. Calculate the net price.
Given: List Price = Ksh 80,000, Trade Discount Rate = 10%
$$ \text{Net Price} = 80,000 \times (1 - \frac{10}{100}) $$$$ = 80,000 \times 0.90 $$$$ = 72,000 $$
Answer: Net Price = Ksh 72,000
Example 2: A retailer is given successive trade discounts of 10% and 5% on goods priced at Ksh 150,000. Calculate the net price.
Given: List Price = Ksh 150,000, Trade Discounts = 10%, 5%
$$ \text{Price after first discount} = 150,000 \times (1 - \frac{10}{100}) = 150,000 \times 0.90 = 135,000 $$
$$ \text{Price after second discount} = 135,000 \times (1 - \frac{5}{100}) = 135,000 \times 0.95 = 128,250 $$
Answer: Net Price = Ksh 128,250
Example 3: A county government office receives an invoice for supplies priced at Ksh 500,000 with successive trade discounts of 8%, 6%, and 4%. Calculate the net price.
Given: List Price = Ksh 500,000, Trade Discounts = 8%, 6%, 4%
$$ \text{After first discount} = 500,000 \times (1 - 0.08) = 500,000 \times 0.92 = 460,000 $$
$$ \text{After second discount} = 460,000 \times (1 - 0.06) = 460,000 \times 0.94 = 432,400 $$
$$ \text{After third discount} = 432,400 \times (1 - 0.04) = 432,400 \times 0.96 = 415,704 $$
Answer: Net Price = Ksh 415,704
Example 4: A SACCO buys printing materials with a list price of Ksh 90,000 and is given a single trade discount of 12%. Calculate the net price.
Given: List Price = Ksh 90,000, Trade Discount = 12%
$$ \text{Net Price} = 90,000 \times (1 - 0.12) = 90,000 \times 0.88 = 79,200 $$
Answer: Net Price = Ksh 79,200
Example 5: A hotel purchases furniture priced at Ksh 250,000 with successive trade discounts of 5%, 3%, and 2%. Calculate the net price.
Given: List Price = Ksh 250,000, Trade Discounts = 5%, 3%, 2%
$$ \text{After first discount} = 250,000 \times 0.95 = 237,500 $$
$$ \text{After second discount} = 237,500 \times 0.97 = 230,375 $$
$$ \text{After third discount} = 230,375 \times 0.98 = 225,768.50 $$
Answer: Net Price = Ksh 225,768.50
Quantity discounts are price reductions offered to buyers who purchase goods in large volumes to encourage bulk buying and reduce inventory costs. The discount rate often increases with the quantity purchased.
The formula to calculate the total price after quantity discount is:
$$ \text{Total Price} = \text{Unit Price} \times \text{Quantity} \times (1 - \frac{\text{Quantity Discount Rate}}{100}) $$
Example 1: A bank orders 100 units of office supplies at Ksh 500 per unit with a 5% quantity discount. Calculate the total price.
Given: Unit Price = Ksh 500, Quantity = 100, Discount Rate = 5%
$$ \text{Total Price} = 500 \times 100 \times (1 - 0.05) = 50,000 \times 0.95 = 47,500 $$
Answer: Total Price = Ksh 47,500
Example 2: A retail business buys 250 units of electronic gadgets at Ksh 1,200 each with a 7% quantity discount. Calculate the total cost.
Given: Unit Price = Ksh 1,200, Quantity = 250, Discount Rate = 7%
$$ \text{Total Price} = 1,200 \times 250 \times (1 - 0.07) = 300,000 \times 0.93 = 279,000 $$
Answer: Total Price = Ksh 279,000
Example 3: A cooperative orders 500 units of fertilizer priced at Ksh 850 per unit with a 10% quantity discount. Calculate the total price.
Given: Unit Price = Ksh 850, Quantity = 500, Discount Rate = 10%
$$ \text{Total Price} = 850 \times 500 \times (1 - 0.10) = 425,000 \times 0.90 = 382,500 $$
Answer: Total Price = Ksh 382,500
Example 4: A hotel purchases 120 chairs at Ksh 3,000 each with a 12% quantity discount. Calculate the total payment.
Given: Unit Price = Ksh 3,000, Quantity = 120, Discount Rate = 12%
$$ \text{Total Price} = 3,000 \times 120 \times (1 - 0.12) = 360,000 \times 0.88 = 316,800 $$
Answer: Total Price = Ksh 316,800
Example 5: A county government office orders 1,000 units of stationery at Ksh 150 per unit with a 15% quantity discount. Calculate the total cost.
Given: Unit Price = Ksh 150, Quantity = 1,000, Discount Rate = 15%
$$ \text{Total Price} = 150 \times 1,000 \times (1 - 0.15) = 150,000 \times 0.85 = 127,500 $$
Answer: Total Price = Ksh 127,500
A retail business receives an invoice of Ksh 60,000 with a 4% cash discount if paid within 14 days. Calculate the cash discount and amount payable. (5 marks)
A SACCO is offered successive trade discounts of 7% and 3% on goods priced at Ksh 180,000. Calculate the net price after discounts. (6 marks)
A bank orders 300 units of printers at Ksh 15,000 each with a 10% quantity discount. Calculate the total amount payable. (6 marks)
A county government office receives an invoice of Ksh 250,000 with a 5% cash discount if paid within 10 days. Calculate the discount and amount payable if paid within the discount period. (5 marks)
A hotel purchases furniture priced at Ksh 400,000 with successive trade discounts of 6%, 4%, and 2%. Calculate the net price. (7 marks)
A cooperative buys 1,200 bags of maize at Ksh 2,000 each with a 12% quantity discount. Calculate the total price payable after discount. (6 marks)
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Create a free accountThis chapter covers essential concepts in commercial mathematics starting with different types of discounts including cash, trade, and quantity discounts, explaining how each affects pricing. It then explores commissions, detailing how they are calculated based on sales performance. Various methods of calculating wages are discussed, focusing on piece rate and hourly rate systems, followed by practical computations of wages and salaries. The chapter introduces the fundamentals of simple and compound interest, providing techniques to find principal, rate, and time using relevant formulas. It also clarifies the differences between profit margin and mark-ups and their impact on pricing strategies. Calculations of gross pay and net pay are presented to demonstrate deductions and take-home earnings. Finally, the chapter addresses depreciation and appreciation of assets, determining hire purchase prices, and computation of foreign exchange transactions, all of which are critical for accurate financial management in business.
A bank offers a cash discount of 5% on an invoice of Ksh 50,000 if payment is made within 10 days. Calculate the amount payable after the discount. (2 marks)
A trading company gives a trade discount of 12% followed by a further 5% on goods worth Ksh 80,000. Find the final price after the discounts. (3 marks)
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