Money - The Mathematics of Everyday Finance
Money is the medium we use to exchange goods and services. Without it, every trade would require finding someone who has exactly what you want and wants exactly what you have – a system called barter that quickly becomes impractical. Money solves this by acting as a universally accepted store of value that anyone can use at any time.
What Money Does
Money serves three key purposes in any economy:
Medium of exchange – it is accepted in payment for goods and services.
Store of value – it holds its worth over time so you can save now and spend later.
Unit of account – it gives us a standard way to measure and compare the value of things.
Types of Money
| Type | Description | Examples |
|---|---|---|
| Coins | Metal discs issued by governments | 1p, 5p, £1, 50 cents |
| Banknotes | Paper or polymer notes | £5, £10, $20, €50 |
| Bank deposits | Money held electronically in accounts | Current account balance |
| Digital / card payments | Electronic transfers between accounts | Debit card, bank transfer |
| Cryptocurrency | Decentralised digital tokens | Bitcoin, Ethereum |
Income and Expenditure
Income is money you receive – wages, salary, freelance earnings, benefits, or interest on savings.
Expenditure is money you spend – rent, food, transport, entertainment, and bills.
The golden rule of personal finance: spend less than you earn.
Profit and Loss
Profit = Selling Price − Cost Price (when selling price is higher)
Loss = Cost Price − Selling Price (when cost price is higher)
Profit percentage = (Profit ÷ Cost Price) × 100
Loss percentage = (Loss ÷ Cost Price) × 100
Worked Examples
Profit = £55 − £40 = £15.
Profit % = (15 / 40) × 100 = 37.5%.
Loss = £300 − £255 = £45.
Loss % = (45 / 300) × 100 = 15%.
Profit = 20% of £85 = 0.20 × 85 = £17.
Selling price = £85 + £17 = £102.
Value Added Tax (VAT)
VAT is a tax added to the selling price of most goods and services. In the UK the standard VAT rate is 20%.
Price including VAT = Original price × 1.20
To find the original price from a VAT-inclusive price: divide by 1.20.
Price with VAT = £750 × 1.20 = £900.
Original price = £216 ÷ 1.20 = £180.
Discounts and Sale Prices
A discount is a reduction on the original price.
Sale price = Original price × (1 − discount rate)
Example: 30% off £60 → £60 × 0.70 = £42.
Common Mistakes
| Mistake | Correction |
|---|---|
| Calculating profit % using selling price as the base | Profit % is always calculated on the cost price |
| Adding VAT to a price that already includes VAT | Check whether the given price is ex-VAT or inc-VAT before calculating |
| Subtracting discount % directly from price without converting to decimal | Convert the percentage to a multiplier first, e.g. 25% off = × 0.75 |
Key Takeaways
- Money acts as a medium of exchange, store of value, and unit of account.
- Profit = Selling Price − Cost Price; Profit % is based on cost price.
- VAT (20% standard UK rate): multiply by 1.20 to add, divide by 1.20 to remove.
- Discount: multiply by (1 − rate) to find the sale price.
Practice Questions
- A trader buys bags for £12 each and sells them for £17. Find the profit percentage.
- A camera worth £420 is sold at a 15% loss. Find the selling price.
- A price of £360 includes 20% VAT. Find the pre-VAT price.
- A shop offers 35% off a £80 pair of shoes. What is the sale price?
- A market stall sells fruit at cost + 40% profit. If the total sales revenue is £280, what was the original cost of the fruit?