Introduction
Financial maths is a crucial topic in GCSE Maths (Years 10-11) that appears across all exam boards (AQA, Edexcel, OCR). It covers real-life money skills like calculating wages, interest, profit, and discounts. This step-by-step guide will help you tackle these problems with confidence, using UK contexts and terminology.
Key Concepts
Before diving into problems, ensure you understand these core ideas:
Wages and Salaries: Pay for work, often hourly or annually.
Simple Interest: Interest calculated only on the original amount.
Compound Interest: Interest calculated on the original amount plus accumulated interest.
Profit and Loss: Difference between selling price and cost price.
Discounts and VAT: Reductions and taxes on prices.
- Exchange Rates: Converting between currencies.
Step-by-Step Approach
1. Wages and Salaries
Example: Sam earns £10.50 per hour. He works 35 hours per week. Calculate his weekly pay.
Solution:
- Multiply hourly rate by hours worked: £10.50 × 35 = £367.50.
If given an annual salary, ÷ by 12 for monthly pay, or by 52 for weekly pay.
2. Simple Interest
Formula: Interest = Principal × Rate × Time
Example: £500 is invested at 3% simple interest per year for 4 years. Calculate the total interest.
Solution:
Interest = 500 × 0.03 × 4 = £60.
- Total amount = £500 + £60 = £560.
3. Compound Interest
Formula: Amount = Principal × (1 + Rate)Time
Example: £800 is invested at 2.5% compound interest per year for 3 years. Find the total amount.
Solution:
- Amount = 800 × (1.025)³ = 800 × 1.076890625 = £861.51 (to 2 d.p.).
4. Profit and Loss
Profit = Selling Price – Cost Price
Loss = Cost Price – Selling Price
Example: A shop buys a shirt for £12 and sells it for £18. Calculate the percentage profit.
Solution:
Profit = £18 – £12 = £6.
- Percentage profit = (Profit ÷ Cost Price) × 100 = (6 ÷ 12) × 100 = 50%.
5. Discounts and VAT
Discount: Reduce price by a percentage.
VAT: Currently 20% in the UK, added to price.
Example: A laptop costs £600 plus VAT. Calculate the total price.
Solution:
VAT = 20% of £600 = £120.
- Total = £600 + £120 = £720.
6. Exchange Rates
Example: £1 = €1.15. Convert £200 to euros.
Solution:
- € = £200 × 1.15 = €230.
Common Mistakes to Avoid
Mixing up simple and compound interest.
Forgetting to convert percentages to decimals (e.g., 5% = 0.05).
Not reading the question carefully (e.g., asking for interest only vs total amount).
- Rounding too early in multi-step problems.
Exam Tips
Always show your working – marks are awarded for method.
Use a calculator for compound interest and complex calculations.
Check units and currency symbols.
- For compound interest, use the power button on your calculator.
Practice Questions
Amy earns £9.80 per hour. She works 22 hours. Calculate her pay.
£1200 is invested at 4% simple interest for 5 years. Find the total interest.
A phone costs £250. In a sale, it is reduced by 15%. Calculate the sale price.
£1500 is invested at 3% compound interest for 2 years. Find the total amount.
- A trader buys 100 pens for £20 and sells them at 50p each. Calculate the percentage profit.
Conclusion
Financial maths is a practical topic that appears frequently in GCSE exams. By following these steps and practising regularly, you can master it. Remember to use UK contexts and always double-check your calculations.
flowchart TD
A["Identify type of problem"] --> B["Wages/Salaries?"]
B -->|Yes| C["Multiply rate by hours"]
B -->|No| D["Interest?"]
D -->|Simple| E["Use I = PRT"]
D -->|Compound| F["Use A = P(1+r)^t"]
D -->|No| G["Profit/Loss?"]
G -->|Yes| H["Calculate difference and percentage"]
G -->|No| I["Discount/VAT?"]
I -->|Yes| J["Calculate percentage and add/subtract"]
I -->|No| K["Exchange Rate?"]
K -->|Yes| L["Multiply by rate"]
- This flowchart summarises the decision process for tackling financial maths problems. Use it as a quick reference during revision.