By the end of this chapter, you will be able to:
These skills will help you confidently handle important financial tasks that keep businesses running smoothly and profitably.
Compiled by: Martin Munene
Commercial business calculations are essential for office administration professionals managing financial transactions, contracts, and budgeting within Kenyan enterprises. Mastery of these calculations enables accurate financial decision-making, effective cash flow management, and proper assessment of business profitability. This chapter focuses on key commercial terms and their application through rigorous numerical problem-solving.
Commercial transactions often involve interest computations, discounts, commissions, and understanding principal and amount values. These concepts form the foundation for daily financial operations in offices such as banks, retail businesses, and government procurement departments. Precise application of these terms ensures correct invoicing, cost estimation, and revenue tracking.
Interest represents the cost of borrowing money or the reward for saving it, typically expressed as a percentage of the principal over time. The two main types are simple interest and compound interest, with simple interest calculated only on the principal and compound interest calculated on the principal plus accumulated interest.
The formula for simple interest is:
$$ I = P \times r \times t $$
where \(I\) is interest, \(P\) is principal, \(r\) is the annual interest rate (decimal), and \(t\) is time in years.
Example 1: A retail business borrows Ksh 50,000 from a SACCO at an annual simple interest rate of 8% for 2 years. Calculate the interest.
Given: \(P = 50,000\) Ksh, \(r = 0.08\), \(t = 2\) years$$I = P \times r \times t$$$$I = 50,000 \times 0.08 \times 2$$$$I = 8,000$$ Answer: Ksh 8,000
Example 2: A school deposits Ksh 30,000 in a bank offering 5% simple interest per annum for 3 years. Find the interest earned.
Given: \(P = 30,000\) Ksh, \(r = 0.05\), \(t = 3\) years$$I = 30,000 \times 0.05 \times 3$$$$I = 4,500$$ Answer: Ksh 4,500
Example 3: A county government office takes a loan of Ksh 120,000 at 10% simple interest per annum for 1.5 years. Calculate the interest payable.
Given: \(P = 120,000\) Ksh, \(r = 0.10\), \(t = 1.5\) years$$I = 120,000 \times 0.10 \times 1.5$$$$I = 18,000$$ Answer: Ksh 18,000
Example 4: Calculate the simple interest on Ksh 75,000 borrowed for 9 months at 12% per annum by a cooperative society.
Given: \(P = 75,000\) Ksh, \(r = 0.12\), \(t = \frac{9}{12} = 0.75\) years$$I = 75,000 \times 0.12 \times 0.75$$$$I = 6,750$$ Answer: Ksh 6,750
Example 5: A hotel takes a loan of Ksh 200,000 at 9% simple interest for 2 years and 6 months. Calculate the interest.
Given: \(P = 200,000\) Ksh, \(r = 0.09\), \(t = 2.5\) years$$I = 200,000 \times 0.09 \times 2.5$$$$I = 45,000$$ Answer: Ksh 45,000
Discounts reduce the price of goods or services to encourage prompt payment or bulk purchases. Trade discounts are offered on the listed price, while cash discounts are incentives for early payment. Calculations involve determining the selling price after applying the discount percentage.
The formula for discount amount is:
$$ D = P \times d $$
where \(D\) is discount, \(P\) is price before discount, and \(d\) is discount rate (decimal).
The net price after discount is:
$$ N = P - D $$
Example 1: A retail store offers a 15% trade discount on an item priced at Ksh 12,000. Calculate the discount and the price after discount.
Given: \(P = 12,000\) Ksh, \(d = 0.15\)$$D = 12,000 \times 0.15$$$$D = 1,800$$$$N = 12,000 - 1,800$$$$N = 10,200$$ Answer: Discount = Ksh 1,800, Price after discount = Ksh 10,200
Example 2: An office supply company gives a 10% cash discount on a Ksh 50,000 invoice if paid within 10 days. Calculate the amount payable if the discount is taken.
Given: \(P = 50,000\) Ksh, \(d = 0.10\)$$D = 50,000 \times 0.10$$$$D = 5,000$$$$N = 50,000 - 5,000$$$$N = 45,000$$ Answer: Ksh 45,000 payable
Example 3: A cooperative sells goods worth Ksh 25,000 with a 12% trade discount and a 5% cash discount. Calculate the final price if both discounts apply.
Given: \(P = 25,000\) Ksh, trade discount \(d_1 = 0.12\), cash discount \(d_2 = 0.05\)
First discount:$$D_1 = 25,000 \times 0.12 = 3,000$$
Price after trade discount:$$P_1 = 25,000 - 3,000 = 22,000$$
Second discount:$$D_2 = 22,000 \times 0.05 = 1,100$$
Final price:$$N = 22,000 - 1,100 = 20,900$$
Answer: Ksh 20,900
Example 4: A hotel offers a 20% trade discount on room bookings amounting to Ksh 80,000 and an additional 3% discount for early payment. Find the amount payable.
Given: \(P = 80,000\) Ksh, trade discount \(d_1 = 0.20\), early payment discount \(d_2 = 0.03\)
Calculate trade discount:$$D_1 = 80,000 \times 0.20 = 16,000$$
Price after trade discount:$$P_1 = 80,000 - 16,000 = 64,000$$
Early payment discount:$$D_2 = 64,000 \times 0.03 = 1,920$$
Final price:$$N = 64,000 - 1,920 = 62,080$$
Answer: Ksh 62,080
Example 5: A school orders stationery worth Ksh 150,000 with a 10% trade discount and a 2% prompt payment discount. Calculate the net amount payable.
Given: \(P = 150,000\), \(d_1 = 0.10\), \(d_2 = 0.02\)
Trade discount:$$D_1 = 150,000 \times 0.10 = 15,000$$
Price after trade discount:$$P_1 = 150,000 - 15,000 = 135,000$$
Prompt payment discount:$$D_2 = 135,000 \times 0.02 = 2,700$$
Net amount:$$N = 135,000 - 2,700 = 132,300$$
Answer: Ksh 132,300
Commissions are payments made to agents or salespersons as a percentage of sales or services rendered. Common in insurance, real estate, and retail sectors, commission calculations often involve fixed or sliding scale rates.
The formula for commission is:
$$ C = S \times c $$
where \(C\) is commission, \(S\) is sales value, and \(c\) is commission rate (decimal).
Example 1: A sales agent earns 5% commission on sales of Ksh 80,000. Calculate the commission.
Given: \(S = 80,000\) Ksh, \(c = 0.05\)$$C = 80,000 \times 0.05$$$$C = 4,000$$ Answer: Ksh 4,000
Example 2: A real estate agent receives 8% commission on a property sold for Ksh 3,000,000. Find the commission.
Given: \(S = 3,000,000\) Ksh, \(c = 0.08\)$$C = 3,000,000 \times 0.08$$$$C = 240,000$$ Answer: Ksh 240,000
Example 3: An insurance agent earns 6% commission on policies sold totaling Ksh 500,000. Calculate the commission.
Given: \(S = 500,000\) Ksh, \(c = 0.06\)$$C = 500,000 \times 0.06$$$$C = 30,000$$ Answer: Ksh 30,000
Example 4: A cooperative society pays 3% commission to agents on monthly savings collections of Ksh 1,200,000. Calculate the commission.
Given: \(S = 1,200,000\) Ksh, \(c = 0.03\)$$C = 1,200,000 \times 0.03$$$$C = 36,000$$ Answer: Ksh 36,000
Example 5: A sales executive gets 4% commission on the first Ksh 100,000 sales and 6% on the balance of Ksh 150,000. Calculate total commission.
Given:
First sales: \(S_1 = 100,000\), \(c_1 = 0.04\)
Balance sales: \(S_2 = 150,000\), \(c_2 = 0.06\)
Calculate commission on first sales:$$C_1 = 100,000 \times 0.04 = 4,000$$
Commission on balance sales:$$C_2 = 150,000 \times 0.06 = 9,000$$
Total commission:$$C = 4,000 + 9,000 = 13,000$$
Answer: Ksh 13,000
Principal is the original sum of money lent, borrowed, or invested, excluding interest. It forms the basis for interest and other financial calculations.
Example 1: A business repays Ksh 12,000 interest on a principal borrowed at 8% simple interest for 3 years. Find the principal.
Given: \(I = 12,000\) Ksh, \(r = 0.08\), \(t = 3\) years
Formula:$$I = P \times r \times t$$
Rearranged:$$P = \frac{I}{r \times t}$$
Substitute:$$P = \frac{12,000}{0.08 \times 3}$$$$P = \frac{12,000}{0.24} = 50,000$$
Answer: Ksh 50,000
Example 2: An investor receives Ksh 9,000 interest from a deposit at 6% per annum after 5 years. Calculate the principal.
Given: \(I = 9,000\), \(r = 0.06\), \(t = 5\)$$P = \frac{9,000}{0.06 \times 5} = \frac{9,000}{0.30} = 30,000$$ Answer: Ksh 30,000
Example 3: A cooperative pays Ksh 15,000 interest at 10% simple interest over 2 years. Find the principal amount.
Given: \(I = 15,000\), \(r = 0.10\), \(t = 2\)$$P = \frac{15,000}{0.10 \times 2} = \frac{15,000}{0.20} = 75,000$$ Answer: Ksh 75,000
Example 4: Calculate the principal if Ksh 6,000 interest was earned at 12% per annum over 4 years.
Given: \(I = 6,000\), \(r = 0.12\), \(t = 4\)$$P = \frac{6,000}{0.12 \times 4} = \frac{6,000}{0.48} = 12,500$$ Answer: Ksh 12,500
Example 5: A business borrows money and pays Ksh 20,000 interest at 7.5% per annum for 8 years. Find the principal.
Given: \(I = 20,000\), \(r = 0.075\), \(t = 8\)$$P = \frac{20,000}{0.075 \times 8} = \frac{20,000}{0.6} = 33,333.33$$ Answer: Ksh 33,333.33
Amount is the total sum payable or receivable after interest is added to the principal. In simple interest, it is the sum of principal and interest.
The formula is:
$$ A = P + I $$
or
$$ A = P (1 + r \times t) $$
Example 1: Calculate the amount payable on a loan of Ksh 25,000 after 4 years at 9% simple interest.
Given: \(P = 25,000\), \(r = 0.09\), \(t = 4\)
Calculate interest:$$I = 25,000 \times 0.09 \times 4 = 9,000$$
Calculate amount:$$A = 25,000 + 9,000 = 34,000$$
Answer: Ksh 34,000
Example 2: An investor deposits Ksh 40,000 for 3 years at 7% simple interest. Find the amount after 3 years.
Given: \(P = 40,000\), \(r = 0.07\), \(t = 3\)$$I = 40,000 \times 0.07 \times 3 = 8,400$$$$A = 40,000 + 8,400 = 48,400$$ Answer: Ksh 48,400
Example 3: A SACCO member borrows Ksh 60,000 at 12% simple interest for 18 months. Calculate the amount to be repaid.
Given: \(P = 60,000\), \(r = 0.12\), \(t = \frac{18}{12} = 1.5\)$$I = 60,000 \times 0.12 \times 1.5 = 10,800$$$$A = 60,000 + 10,800 = 70,800$$ Answer: Ksh 70,800
Example 4: Calculate the amount payable on a loan of Ksh 100,000 after 2.5 years at 6% simple interest.
Given: \(P = 100,000\), \(r = 0.06\), \(t = 2.5\)$$I = 100,000 \times 0.06 \times 2.5 = 15,000$$$$A = 100,000 + 15,000 = 115,000$$ Answer: Ksh 115,000
Example 5: A business invests Ksh 85,000 at 10% simple interest for 5 years. Find the amount at the end of the period.
Given: \(P = 85,000\), \(r = 0.10\), \(t = 5\)$$I = 85,000 \times 0.10 \times 5 = 42,500$$$$A = 85,000 + 42,500 = 127,500$$ Answer: Ksh 127,500
Compound interest is interest calculated on the initial principal and also on accumulated interest from previous periods. It is common in savings, investments, and long-term loans.
The formula for amount with compound interest is:
$$ A = P \times (1 + r)^t $$
Interest earned is:
$$ I = A - P $$
where \(P\) is principal, \(r\) is interest rate per period, and \(t\) is number of periods.
Example 1: An office invests Ksh 20,000 at 10% compound interest per annum for 2 years. Calculate the amount.
Given: \(P = 20,000\), \(r = 0.10\), \(t = 2\)$$A = 20,000 \times (1 + 0.10)^2 = 20,000 \times 1.21 = 24,200$$ Answer: Ksh 24,200
Example 2: Calculate the compound interest on Ksh 50,000 invested at 8% per annum for 3 years.
Given: \(P = 50,000\), \(r = 0.08\), \(t = 3\)$$A = 50,000 \times (1 + 0.08)^3 = 50,000 \times 1.259712 = 62,985.60$$$$I = 62,985.60 - 50,000 = 12,985.60$$ Answer: Ksh 12,985.60
Example 3: A cooperative saves Ksh 100,000 at 12% compound interest annually for 4 years. Find the amount and interest.
Given: \(P = 100,000\), \(r = 0.12\), \(t = 4\)$$A = 100,000 \times (1 + 0.12)^4 = 100,000 \times 1.573519 = 157,351.90$$$$I = 157,351.90 - 100,000 = 57,351.90$$ Answer: Amount = Ksh 157,351.90; Interest = Ksh 57,351.90
Example 4: A county government invests Ksh 80,000 at 9% compound interest for 5 years. Calculate the final amount.
Given: \(P = 80,000\), \(r = 0.09\), \(t = 5\)$$A = 80,000 \times (1 + 0.09)^5 = 80,000 \times 1.53862 = 123,089.60$$ Answer: Ksh 123,089.60
Example 5: Calculate the compound interest on Ksh 150,000 invested at 7% per annum for 6 years.
Given: \(P = 150,000\), \(r = 0.07\), \(t = 6\)$$A = 150,000 \times (1 + 0.07)^6 = 150,000 \times 1.50073 = 225,109.50$$$$I = 225,109.50 - 150,000 = 75,109.50$$ Answer: Ksh 75,109.50
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Create a free accountThis chapter covers essential terms used in commercial business calculations, including interests, discounts, commissions, principal, amount, and compound interest. It begins with an explanation of simple interest, focusing on its meaning and how to calculate it accurately. The components of compound interest are then discussed, highlighting the interest rate, principal, number of compounding periods in a year, and time. The process of calculating compound interest is detailed, including converting the interest rate and determining the values of principal, rate, number of periods, and time before substitution. Sales discount calculations follow, covering trade discounts, cash discounts, and quantity discounts. Finally, the chapter addresses different types of sales commissions, such as flat commission, tiered commission, bonus structures, and gross profit commission, providing methods for their calculation. This comprehensive overview equips learners with practical skills to perform various commercial business calculations confidently.
An office manager invests Ksh 50,000 in a fixed deposit account at a simple interest rate of 8% per annum. Calculate the interest earned after 3 years. (3 marks)
A stationery supplier offers a trade discount of 12% on an order worth Ksh 120,000. Calculate the amount payable after the trade discount. (3 marks)
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