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Subject Combination 3% exam weight

Topic 10

Part of the Post-UTME (Nigeria) study roadmap. Subject Combination topic subjec-010 of Subject Combination.

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Commercial Mathematics

Commercial mathematics covers the mathematical concepts used in business, trade, and financial transactions. For the Post-UTME examination, you need to master topics including simple and compound interest, hire purchase, depreciation, profit and loss calculations, taxation, and exchange rates. These are practical, everyday math skills essential for commerce students.

Simple Interest

Simple Interest (SI) is calculated only on the original principal amount.

Formula: SI = (P × R × T) / 100 Where: P = Principal, R = Rate per annum (%), T = Time in years

Amount (A) = Principal + Simple Interest = P + SI = P(1 + RT/100)

Example: ₦5,000 invested at 8% per annum for 3 years. SI = (5000 × 8 × 3)/100 = (5000 × 24)/100 = ₦1,200 Amount = 5000 + 1200 = ₦6,200

Finding Principal, Rate, or Time

  • P = (SI × 100) / (R × T)
  • R = (SI × 100) / (P × T)
  • T = (SI × 100) / (P × R)

Compound Interest

Compound Interest (CI) is calculated on the accumulated principal (including previous interest).

Formula: A = P(1 + R/100)^T CI = A − P

Compounding more frequently (half-yearly, quarterly, monthly): A = P(1 + R/(100n))^(nT) where n = number of compounding periods per year.

Example: ₦10,000 at 10% per annum compound interest for 3 years. Year 1: 10,000 × 1.10 = 11,000 Year 2: 11,000 × 1.10 = 12,100 Year 3: 12,100 × 1.10 = ₦13,310 CI = 13,310 − 10,000 = ₦3,310

(Compare Simple Interest: SI = (10000×10×3)/100 = ₦3,000)

Depreciation

Depreciation is the decrease in value of an asset over time due to wear and tear or obsolescence.

Straight Line Method

Annual Depreciation = (Cost − Salvage Value) / Useful Life Example: Machine costs ₦50,000, salvage value ₦5,000, useful life 5 years. Annual depreciation = (50000 − 5000)/5 = ₦9,000 per year

Reducing Balance Method (Declining Balance)

Depreciation = Rate × Book value at beginning of year

Example: Asset value ₦100,000, depreciation rate 20% per year. Year 1: Depreciation = 0.20 × 100,000 = ₦20,000; Book value = ₦80,000 Year 2: Depreciation = 0.20 × 80,000 = ₦16,000; Book value = ₦64,000 Year 3: Depreciation = 0.20 × 64,000 = ₦12,800; Book value = ₦51,200

Hire Purchase

Hire Purchase (HP) is a method of buying goods where the buyer pays a deposit followed by installments. Interest is charged on the outstanding balance.

Total Amount Paid = Deposit + (Monthly Installment × Number of installments) HP Interest = Total Amount Paid − Cash Price

Example: A generator costs ₦80,000 cash or ₦15,000 deposit plus 12 monthly installments of ₦6,500.

  • Total amount paid = 15,000 + (12 × 6,500) = 15,000 + 78,000 = ₦93,000
  • HP Interest = 93,000 − 80,000 = ₦13,000
  • Effective interest rate ≈ (13000/80000) × 100 = 16.25%

Taxation

Sales Tax / Value Added Tax (VAT)

VAT is a tax on the value added at each stage of production.

Example: A product costs ₦5,000 before VAT at 7.5%. VAT amount = 5000 × 7.5% = ₦375 Price including VAT = 5000 + 375 = ₦5,375

Withholding Tax

A tax deducted at source from payments for services or dividends.

Example: A professional receives ₦200,000 for services and withholding tax is 10%. Tax withheld = 200,000 × 10% = ₦20,000 Amount received = 200,000 − 20,000 = ₦180,000

Income Tax Basics

Personal income tax is typically calculated on a graduated scale (tax brackets).

Example: If income is ₦600,000 and tax is charged at 10% on the first ₦300,000 and 15% on the balance: Tax = (0.10 × 300,000) + (0.15 × 300,000) = 30,000 + 45,000 = ₦75,000

Foreign Exchange

Exchange rates express the value of one currency in terms of another.

Conversion

Example: If ₦1 = $0.0025, convert ₦200,000 to dollars. Dollars = 200,000 × 0.0025 = $500

Example: If the exchange rate changes to ₦1 = $0.003, how much more dollars from the same ₦200,000? New amount = 200,000 × 0.003 = $600 → $100 more

Commission and Brokerage

Commission is a fee paid to an agent or broker for services rendered, usually calculated as a percentage of the transaction value.

Example: A sales agent earns 5% commission on all sales. If he sold goods worth ₦2,400,000 in a month, what is his commission? Commission = 2,400,000 × 5% = ₦120,000

Net proceeds = Selling price − Commission

Key Post-UTME Exam Facts

  • Simple Interest: SI = PRT/100; A = P(1 + RT/100)
  • Compound Interest: A = P(1 + R/100)^T; CI = A − P
  • Depreciation (straight line): (Cost − Salvage)/Useful Life
  • Hire Purchase: Total paid = Deposit + Installments; HP Interest = Total paid − Cash price
  • VAT: Price including VAT = Price × (1 + VAT rate)
  • Commission: Commission = Transaction value × Commission rate
  • ⚡ Exam tip: Compound interest always gives MORE than simple interest for periods > 1 year. Always check whether the question asks for SI or CI!

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

  • Simple Interest: SI = PRT/100; straightforward calculation on original principal
  • Compound Interest: A = P(1+R/100)^T; interest on accumulated amount
  • Depreciation: Straight line = (Cost−Salvage)/Years; Reducing balance = Rate × Book value
  • Hire Purchase: Watch for deposit + installments; HP Interest = Total − Cash Price
  • VAT: Added to price; 7.5% VAT means multiply by 1.075
  • Commission: Percentage of transaction value
  • ⚡ Exam tip: For “how long to double” questions with simple interest: T = 100/R years (since SI = P×R×T/100 = P when T = 100/R)

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Comparing Simple and Compound Interest

Example: ₦50,000 at 12% per annum for 3 years:

  • Simple Interest: SI = (50000×12×3)/100 = ₦18,000
  • Compound Interest (annual):
    • Year 1: 50000×1.12 = 56,000
    • Year 2: 56000×1.12 = 62,720
    • Year 3: 62720×1.12 = 70,246.40
    • CI = 70,246.40 − 50,000 = ₦20,246.40

Compound interest gives ₦2,246.40 more than simple interest.

Profit and Loss in Commercial Mathematics

  • Mark-up: Adding to cost price to get selling price → Mark-up % = (Mark-up/Cost) × 100
  • Margin: Profit as a percentage of selling price → Margin % = (Profit/SP) × 100

Example: A trader buys goods at ₦200 and sells at ₦250.

  • Profit = ₦50
  • Mark-up on cost = (50/200) × 100 = 25%
  • Margin on selling = (50/250) × 100 = 20%

Note: Mark-up % and Margin % are NOT the same thing!

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Annuities

An annuity is a series of equal payments made at regular intervals.

Future Value of an Annuity (Regular Payments)

If you save ₦A at the end of each year at rate r%: Future Value = A × [(1+r)^n − 1]/r

Example: ₦10,000 saved at end of each year at 8% for 5 years. FV = 10000 × [(1.08)^5 − 1]/0.08 = 10000 × [1.4693 − 1]/0.08 = 10000 × 0.4693/0.08 = ₦58,666

Insurance Mathematics

Life Insurance Premium

Life insurance premium is based on the concept of probability of death at different ages (mortality tables).

Net Premium = Sum assured × Probability of death at that age

Property Insurance

Premium = Value of property × Rate per ₦1,000 × (1 + loading factor)

Break-Even Analysis

Break-even point: The level of sales at which total revenue = total costs (profit = 0).

Break-even quantity = Fixed Costs / (Selling Price per unit − Variable Cost per unit) Break-even revenue = Fixed Costs / Contribution Margin Ratio

Example: Fixed costs = ₦100,000; Selling price = ₦500 per unit; Variable cost = ₦300 per unit. Contribution per unit = 500 − 300 = ₦200 Break-even quantity = 100,000/200 = 500 units Break-even revenue = 100,000/(200/500) = ₦250,000

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