Compiled by: Collins Onyango
Commercial business calculations are essential skills for office administration professionals in Kenya, enabling accurate financial management, pricing, and decision-making within various organizations such as banks, retail businesses, and county government offices. Mastery of these calculations supports efficient handling of interests, discounts, commissions, and related financial terms that frequently arise in commercial transactions. This chapter develops these competencies through focused mathematical methods and practical examples grounded in real-world office administration contexts.
This section covers key commercial terms and their mathematical treatment. It enables office administrators to perform precise calculations necessary for financial documentation, billing, and reporting.
Interest calculations are fundamental for determining the cost of borrowed money or the return on investments, frequently encountered when managing loans or deposits in banks and SACCOs. The two main types of interest calculations are simple interest and compound interest.
Simple interest is calculated on the original principal amount only over a specified period.
$$ SI = \frac{P \times R \times T}{100} $$
where \(SI\) = simple interest, \(P\) = principal amount (Ksh), \(R\) = rate of interest (% per annum), \(T\) = time (years).
Example 1: A county government office borrows Ksh 100,000 at 8% simple interest per annum for 3 years. Calculate the interest.
Given: \(P = 100,000\) Ksh, \(R = 8\%\), \(T = 3\) years$$ SI = \frac{100,000 \times 8 \times 3}{100} $$$$ SI = \frac{2,400,000}{100} $$$$ SI = 24,000 \text{ Ksh} $$ Answer: Ksh 24,000
Example 2: A SACCO member deposits Ksh 50,000 at 10% simple interest for 2.5 years. Find the interest earned.
Given: \(P = 50,000\) Ksh, \(R = 10\%\), \(T = 2.5\) years$$ SI = \frac{50,000 \times 10 \times 2.5}{100} $$$$ SI = \frac{1,250,000}{100} $$$$ SI = 12,500 \text{ Ksh} $$ Answer: Ksh 12,500
Example 3: A retail shop owner borrows Ksh 120,000 at 6% simple interest for 1 year 8 months. Calculate the interest.
Given: \(P = 120,000\) Ksh, \(R = 6\%\), \(T = \frac{20}{12} = 1.6667\) years$$ SI = \frac{120,000 \times 6 \times 1.6667}{100} $$$$ SI = \frac{1,200,000}{100} $$$$ SI = 12,000 \text{ Ksh} $$ Answer: Ksh 12,000
Compound interest is calculated on the principal plus the accumulated interest over previous periods, common in bank savings and investment accounts.
$$ A = P \times (1 + \frac{R}{100})^T $$$$ CI = A - P $$
where \(A\) = amount, \(CI\) = compound interest, \(P\) = principal, \(R\) = rate (% per annum), \(T\) = time (years).
Example 1: A cooperative deposits Ksh 80,000 at 5% compound interest for 2 years. Calculate the amount and compound interest.
Given: \(P = 80,000\) Ksh, \(R = 5\%\), \(T = 2\) years$$ A = 80,000 \times (1 + \frac{5}{100})^2 $$$$ A = 80,000 \times (1.05)^2 $$$$ A = 80,000 \times 1.1025 $$$$ A = 88,200 \text{ Ksh} $$$$ CI = 88,200 - 80,000 = 8,200 \text{ Ksh} $$ Answer: Amount = Ksh 88,200; Compound Interest = Ksh 8,200
Example 2: A hotel invests Ksh 150,000 at 6% compound interest for 3 years. Calculate the amount.
Given: \(P = 150,000\) Ksh, \(R = 6\%\), \(T = 3\) years$$ A = 150,000 \times (1 + \frac{6}{100})^3 $$$$ A = 150,000 \times (1.06)^3 $$$$ A = 150,000 \times 1.191016 $$$$ A = 178,652.4 \text{ Ksh} $$ Answer: Ksh 178,652.40
Example 3: A bank offers 8% compound interest compounded annually. Calculate the amount on Ksh 200,000 after 4 years.
Given: \(P = 200,000\) Ksh, \(R = 8\%\), \(T = 4\) years$$ A = 200,000 \times (1 + \frac{8}{100})^4 $$$$ A = 200,000 \times (1.08)^4 $$$$ A = 200,000 \times 1.3605 $$$$ A = 272,100 \text{ Ksh} $$ Answer: Ksh 272,100
Discounts reduce the selling price of goods or services and are common in retail, wholesale, and procurement activities managed by office administrators.
Trade discount is a reduction from the list price offered by wholesalers or manufacturers.
$$ \text{Trade Discount} = \text{List Price} \times \frac{\text{Discount \%}}{100} $$
Example 1: A retail store buys goods listed at Ksh 40,000 with a 10% trade discount. Find the amount to pay.
Given: List Price = Ksh 40,000, Discount = 10%$$ \text{Trade Discount} = 40,000 \times \frac{10}{100} $$$$ = 4,000 \text{ Ksh} $$$$ \text{Net Price} = 40,000 - 4,000 = 36,000 \text{ Ksh} $$ Answer: Ksh 36,000
Example 2: A county office orders equipment worth Ksh 120,000 with a 15% trade discount. Calculate the amount payable.
Given: List Price = Ksh 120,000, Discount = 15%$$ \text{Trade Discount} = 120,000 \times \frac{15}{100} $$$$ = 18,000 \text{ Ksh} $$$$ \text{Net Price} = 120,000 - 18,000 = 102,000 \text{ Ksh} $$ Answer: Ksh 102,000
Example 3: A supplier offers a 12% trade discount on goods priced Ksh 75,000. What is the discounted price?
Given: List Price = Ksh 75,000, Discount = 12%$$ \text{Trade Discount} = 75,000 \times \frac{12}{100} $$$$ = 9,000 \text{ Ksh} $$$$ \text{Net Price} = 75,000 - 9,000 = 66,000 \text{ Ksh} $$ Answer: Ksh 66,000
Cash discount is allowed for early payment and calculated on the invoice amount after trade discount.
$$ \text{Cash Discount} = \text{Invoice Amount} \times \frac{\text{Discount \%}}{100} $$
Example 1: A supplier offers a 5% cash discount on Ksh 36,000 if paid within 10 days. Calculate the cash discount and amount payable.
Given: Invoice Amount = Ksh 36,000, Discount = 5%$$ \text{Cash Discount} = 36,000 \times \frac{5}{100} $$$$ = 1,800 \text{ Ksh} $$$$ \text{Amount Payable} = 36,000 - 1,800 = 34,200 \text{ Ksh} $$ Answer: Cash Discount = Ksh 1,800; Amount Payable = Ksh 34,200
Example 2: A school pays an invoice of Ksh 102,000 within the discount period with a 3% cash discount. Find the payable amount.
Given: Invoice Amount = Ksh 102,000, Discount = 3%$$ \text{Cash Discount} = 102,000 \times \frac{3}{100} $$$$ = 3,060 \text{ Ksh} $$$$ \text{Amount Payable} = 102,000 - 3,060 = 98,940 \text{ Ksh} $$ Answer: Ksh 98,940
Example 3: A university receives an invoice of Ksh 66,000 with a 4% cash discount for early payment. Calculate the discount and net payment.
Given: Invoice Amount = Ksh 66,000, Discount = 4%$$ \text{Cash Discount} = 66,000 \times \frac{4}{100} $$$$ = 2,640 \text{ Ksh} $$$$ \text{Amount Payable} = 66,000 - 2,640 = 63,360 \text{ Ksh} $$ Answer: Ksh 63,360
Commissions are payments made to agents or salespersons as a percentage of sales or transactions, important for payroll and sales management in businesses.
Commission is calculated as:
$$ \text{Commission} = \text{Sales Value} \times \frac{\text{Commission Rate \%}}{100} $$
Example 1: A salesperson sells goods worth Ksh 150,000 with a 6% commission. Calculate the commission earned.
Given: Sales Value = Ksh 150,000, Commission Rate = 6%$$ \text{Commission} = 150,000 \times \frac{6}{100} $$$$ = 9,000 \text{ Ksh} $$ Answer: Ksh 9,000
Example 2: An agent earns 8% commission on Ksh 320,000 sales. Find the commission amount.
Given: Sales Value = Ksh 320,000, Commission Rate = 8%$$ \text{Commission} = 320,000 \times \frac{8}{100} $$$$ = 25,600 \text{ Ksh} $$ Answer: Ksh 25,600
Example 3: A cooperative pays 5% commission on Ksh 500,000 sales. Calculate the commission.
Given: Sales Value = Ksh 500,000, Commission Rate = 5%$$ \text{Commission} = 500,000 \times \frac{5}{100} $$$$ = 25,000 \text{ Ksh} $$ Answer: Ksh 25,000
Sometimes commission is based on cost price, other times on selling price.
$$ \text{Commission} = \text{Base Amount} \times \frac{\text{Rate}}{100} $$
where Base Amount is either Cost Price or Selling Price.
Example 1: A sales agent gets 7% commission on cost price of Ksh 200,000. Calculate commission.
Given: Cost Price = Ksh 200,000, Rate = 7%$$ \text{Commission} = 200,000 \times \frac{7}{100} $$$$ = 14,000 \text{ Ksh} $$ Answer: Ksh 14,000
Example 2: An agent receives 6% commission on selling price of Ksh 250,000. Calculate commission.
Given: Selling Price = Ksh 250,000, Rate = 6%$$ \text{Commission} = 250,000 \times \frac{6}{100} $$$$ = 15,000 \text{ Ksh} $$ Answer: Ksh 15,000
Example 3: A dealer pays 5% commission on cost price of Ksh 400,000. Find the commission.
Given: Cost Price = Ksh 400,000, Rate = 5%$$ \text{Commission} = 400,000 \times \frac{5}{100} $$$$ = 20,000 \text{ Ksh} $$ Answer: Ksh 20,000
The principal is the original sum of money lent, borrowed, or invested before interest.
Principal is the base amount on which interest is calculated.
$$ SI = \frac{P \times R \times T}{100} $$
Example 1: Find the principal if simple interest is Ksh 4,800 at 6% for 4 years.
Given: \(SI = 4,800\), \(R = 6\%\), \(T = 4\) years$$ P = \frac{SI \times 100}{R \times T} $$$$ P = \frac{4,800 \times 100}{6 \times 4} $$$$ P = \frac{480,000}{24} $$$$ P = 20,000 \text{ Ksh} $$ Answer: Ksh 20,000
Example 2: Simple interest is Ksh 12,000 at 8% for 5 years. Find principal.
Given: \(SI = 12,000\), \(R = 8\%\), \(T = 5\) years$$ P = \frac{12,000 \times 100}{8 \times 5} $$$$ P = \frac{1,200,000}{40} $$$$ P = 30,000 \text{ Ksh} $$ Answer: Ksh 30,000
Example 3: Interest of Ksh 9,600 was earned at 12% for 2 years. Calculate principal.
Given: \(SI = 9,600\), \(R = 12\%\), \(T = 2\) years$$ P = \frac{9,600 \times 100}{12 \times 2} $$$$ P = \frac{960,000}{24} $$$$ P = 40,000 \text{ Ksh} $$ Answer: Ksh 40,000
Principal is the initial investment before accumulation.
$$ A = P \times (1 + \frac{R}{100})^T $$
Example 1: Amount after 3 years is Ksh 11,340 at 10% compound interest. Find principal.
Given: \(A = 11,340\), \(R = 10\%\), \(T = 3\) years$$ P = \frac{A}{(1 + \frac{R}{100})^T} $$$$ P = \frac{11,340}{(1.10)^3} $$$$ P = \frac{11,340}{1.331} $$$$ P = 8,520.67 \text{ Ksh} $$ Answer: Ksh 8,520.67
Example 2: Amount after 2 years is Ksh 14,400 at 8% compound interest. Find principal.
Given: \(A = 14,400\), \(R = 8\%\), \(T = 2\) years$$ P = \frac{14,400}{(1.08)^2} $$$$ P = \frac{14,400}{1.1664} $$$$ P = 12,346.94 \text{ Ksh} $$ Answer: Ksh 12,346.94
Example 3: Amount is Ksh 50,653 after 4 years at 12%. Calculate principal.
Given: \(A = 50,653\), \(R = 12\%\), \(T = 4\) years$$ P = \frac{50,653}{(1.12)^4} $$$$ P = \frac{50,653}{1.5735} $$$$ P = 32,200 \text{ Ksh} $$ Answer: Ksh 32,200
The amount is the total sum after interest is added to the principal.
$$ A = P + SI $$
Example 1: Principal is Ksh 15,000, simple interest is Ksh 3,000. Find amount.
Given: \(P = 15,000\), \(SI = 3,000\)$$ A = 15,000 + 3,000 $$$$ A = 18,000 \text{ Ksh} $$ Answer: Ksh 18,000
Example 2: Principal Ksh 40,000, simple interest Ksh 4,800. Calculate amount.
Given: \(P = 40,000\), \(SI = 4,800\)$$ A = 40,000 + 4,800 $$$$ A = 44,800 \text{ Ksh} $$ Answer: Ksh 44,800
Example 3: Principal Ksh 25,000, interest Ksh 2,250. Find total amount.
Given: \(P = 25,000\), \(SI = 2,250\)$$ A = 25,000 + 2,250 $$$$ A = 27,250 \text{ Ksh} $$ Answer: Ksh 27,250
$$ A = P \times (1 + \frac{R}{100})^T $$
Example 1: Principal Ksh 30,000 at 7% for 3 years. Find amount.
Given: \(P = 30,000\), \(R = 7\%\), \(T = 3\) years$$ A = 30,000 \times (1.07)^3 $$$$ A = 30,000 \times 1.225043 $$$$ A = 36,751.29 \text{ Ksh} $$ Answer: Ksh 36,751.29
Example 2: Principal Ksh 45,000 at 9% for 2 years. Find amount.
Given: \(P = 45,000\), \(R = 9\%\), \(T = 2\) years$$ A = 45,000 \times (1.09)^2 $$$$ A = 45,000 \times 1.1881 $$$$ A = 53,464.50 \text{ Ksh} $$ Answer: Ksh 53,464.50
Example 3: Principal Ksh 55,000 at 10% for 4 years. Calculate amount.
Given: \(P = 55,000\), \(R = 10\%\), \(T = 4\) years$$ A = 55,000 \times (1.10)^4 $$$$ A = 55,000 \times 1.4641 $$$$ A = 80,525.50 \text{ Ksh} $$ Answer: Ksh 80,525.50
Compound interest calculations are critical for managing investments and loans where interest is compounded annually or more frequently.
$$ A = P \times (1 + \frac{R}{100})^T $$$$ CI = A - P $$
Example 1: Calculate compound interest on Ksh 100,000 at 6% for 3 years.
Given: \(P = 100,000\), \(R = 6\%\), \(T = 3\) years$$ A = 100,000 \times (1.06)^3 $$$$ A = 100,000 \times 1.191016 $$$$ A = 119,101.60 \text{ Ksh} $$$$ CI = 119,101.60 - 100,000 = 19,101.60 \text{ Ksh} $$ Answer: Compound Interest = Ksh 19,101.60
Example 2: Find compound interest on Ksh 250,000 at 8% for 4 years.
Given: \(P = 250,000\), \(R = 8\%\), \(T = 4\) years$$ A = 250,000 \times (1.08)^4 $$$$ A = 250,000 \times 1.3605 $$$$ A = 340,125 \text{ Ksh} $$$$ CI = 340,125 - 250,000 = 90,125 \text{ Ksh} $$ Answer: Compound Interest = Ksh 90,125
Example 3: A SACCO member invests Ksh 60,000 at 10% compound interest for 5 years. Find compound interest.
Given: \(P = 60,000\), \(R = 10\%\), \(T = 5\) years$$ A = 60,000 \times (1.10)^5 $$$$ A = 60,000 \times 1.61051 $$$$ A = 96,630.60 \text{ Ksh} $$$$ CI = 96,630.60 - 60,000 = 36,630.60 \text{ Ksh} $$ Answer: Compound Interest = Ksh 36,630.60
When interest is compounded more than once a year (semi-annually, quarterly), the formula adjusts:
$$ A = P \times (1 + \frac{R}{100 \times n})^{n \times T} $$
where \(n\) = number of compounding periods per year.
Example 1: Calculate amount on Ksh 50,000 at 12% compounded semi-annually for 2 years.
Given: \(P = 50,000\), \(R = 12\%\), \(T = 2\), \(n = 2\)$$ A = 50,000 \times (1 + \frac{12}{100 \times 2})^{2 \times 2} $$$$ A = 50,000 \times (1 + 0.06)^4 $$$$ A = 50,000 \times (1.06)^4 $$$$ A = 50,000 \times 1.2625 $$$$ A = 63,125 \text{ Ksh} $$ Answer: Ksh 63,125
Example 2: Find amount on Ksh 80,000 at 10% compounded quarterly for 3 years.
Given: \(P = 80,000\), \(R = 10\%\), \(T = 3\), \(n = 4\)$$ A = 80,000 \times (1 + \frac{10}{100 \times 4})^{4 \times 3} $$$$ A = 80,000 \times (1 + 0.025)^{12} $$$$ A = 80,000 \times (1.025)^{12} $$$$ A = 80,000 \times 1.3449 $$$$ A = 107,592 \text{ Ksh} $$ Answer: Ksh 107,592
Example 3: Calculate compound interest on Ksh 100,000 at 8% compounded monthly for 1 year.
Given: \(P = 100,000\), \(R = 8\%\), \(T = 1\), \(n = 12\)$$ A = 100,000 \times (1 + \frac{8}{100 \times 12})^{12 \times 1} $$$$ A = 100,000 \times (1 + 0.006667)^{12} $$$$ A = 100,000 \times (1.006667)^{12} $$$$ A = 100,000 \times 1.083 $$$$ A = 108,300 \text{ Ksh} $$$$ CI = 108,300 - 100,000 = 8,300 \text{ Ksh} $$ Answer: Compound Interest = Ksh 8,300
Create a free account to open more of this chapter.
Free: practical guides, quick cards, workplace scenarios and more.
Create a free accountThis chapter covers essential commercial business calculations, beginning with key terms such as interest, discounts, commissions, principal, amount, and compound interest. It explains simple interest, including its meaning and calculation methods. The chapter then details the components of compound interest, focusing on the interest rate, principal, number of compounding periods per year, and time. It guides learners through calculating compound interest by converting interest rates, determining values for principal, rate, compounding frequency, and time, and substituting these into formulas to find the interest. The chapter also addresses sales discounts, distinguishing trade, cash, and quantity discounts and their calculations. Finally, it explores various sales commission calculations, covering flat commission, tiered commission, bonus structures, and gross profit commissions, providing a comprehensive understanding of commercial business computations.
Calculate the simple interest on a loan of Ksh 50,000 borrowed for 2 years at an annual interest rate of 8%. (3 marks)
An office equipment supplier offers a trade discount of 15% on a machine priced at Ksh 120,000. Calculate the amount payable after the trade discount. (3 marks)