Money & Finance
Profit and Loss
When a business sells goods, the key question is: did they make money or lose it?
Profit = Selling price − Cost price (when selling price > cost price) Loss = Cost price − Selling price (when cost price > selling price)
Worked Example: An item costs £40 to make and sells for £52.
- Profit = £52 - £40 = £12
To express this as a percentage of the cost: Profit % = (Profit / Cost price) × 100
- Profit % = (12 / 40) × 100 = 30%
Worked Example (Loss): Bought for £150, sold for £120.
- Loss = £150 - £120 = £30
- Loss % = (30 / 150) × 100 = 20%
Key Terms
- Cost price — what it costs to make or buy the item
- Selling price — what the customer pays
- Revenue — total money received from sales
- Margin — profit expressed as a percentage of the selling price (not cost)
Simple Interest
Simple interest is earned on the original principal only — it does not grow over time.
I = P × R × T / 100
Where:
- P = principal (starting amount)
- R = annual interest rate (%)
- T = time in years
Worked Example: £500 invested at 4% per year for 3 years:
- I = 500 × 4 × 3 / 100 = £60
- Total after 3 years = £500 + £60 = £560
Worked Example: £800 at 3% for 4 years:
- I = 800 × 3 × 4 / 100 = £96
Compound Interest
Compound interest is added to the principal each period, so the next period earns interest on the new (larger) total. Interest earns interest.
A = P × (1 + r/100)ⁿ
Where:
- A = final amount
- P = principal
- r = annual interest rate (%)
- n = number of years
Worked Example: £1,000 at 5% for 2 years:
- Year 1: £1,000 × 1.05 = £1,050
- Year 2: £1,050 × 1.05 = £1,102.50
- Using the formula: A = 1,000 × 1.05² = 1,000 × 1.1025 = £1,102.50
Compare to simple interest: £1,000 at 5% for 2 years = £100 interest → only £1,100. Compound interest gives £2.50 more because the first year's interest also earns interest in year 2.
Over longer periods, the difference between simple and compound interest becomes very significant.
VAT (Value Added Tax)
VAT is a government tax added to the price of most goods and services. In the UK, the standard rate is 20%.
Adding VAT: multiply the original price by 1.20
- £90 + 20% VAT = £90 × 1.20 = £108
Removing VAT (finding the pre-VAT price): divide by 1.20
- Price including VAT is £120. Pre-VAT = £120 ÷ 1.20 = £100
Percentage Change
Many financial problems involve percentage increases or decreases:
% Change = (Change / Original) × 100
- Price rises from £80 to £100: % increase = (20/80) × 100 = 25%
- Price falls from £200 to £150: % decrease = (50/200) × 100 = 25%
Worked Example: A phone originally costs £320 and is reduced by 15%. Find the sale price.
- 15% of £320 = £48
- Sale price = £320 - £48 = £272
- Or: £320 × 0.85 = £272 (multiply by 1 - 0.15 = 0.85)
Budgeting
A budget is a plan for income and expenditure over a period of time.
Surplus = Income − Expenditure (positive result) Deficit = Income − Expenditure (negative result)
Example Budget:
| Category | Monthly Amount |
|---|---|
| Salary (income) | £2,000 |
| Rent | £700 |
| Food | £250 |
| Transport | £100 |
| Bills | £150 |
| Total expenditure | £1,200 |
| Surplus | £800 |
A surplus means money is left over for savings or discretionary spending. A deficit means you are spending more than you earn.
Common Mistakes
- Mistake: calculating profit percentage using the selling price instead of the cost price. Fix: always divide by the cost price for profit %.
- Mistake: confusing simple and compound interest. Fix: simple interest only uses the original principal every time; compound interest uses the growing total.
- Mistake: removing VAT by subtracting 20%. Fix: divide by 1.20, not subtract 20%. (Subtracting 20% of the VAT-inclusive price gives a slightly wrong answer.)
- Mistake: writing a budget deficit as a positive number. Fix: expenditure > income = deficit = negative balance.
Tips and Tricks
- For compound interest calculations, remember (1 + r/100)ⁿ — the base is always 1 plus the decimal rate.
- A quick check: compound interest should always give more than simple interest for the same rate and time.
- To find 20% quickly: find 10% (divide by 10) and double it.
- Always label your profit/loss as a percentage of the cost price unless the question specifies otherwise.