Year 9: Financial mathematics

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1. What is financial mathematics?

Financial mathematics involves applying mathematical methods to solve problems related to money. This includes calculating discounts, interest, profit, budgeting, and tax.

2. Earning money

People earn money through different types of income:

• Wages: Paid per hour or per day worked
• Salary: Fixed annual amount, paid regularly (e.g., fortnightly)
• Commission: A percentage of sales
• Overtime: Extra pay for hours worked beyond the normal working hours

3. Budgeting

A budget is a plan for managing income and expenses. It helps you control your spending and save for future goals.

• Income: Money received
• Expenses: Money spent
• Savings: Income − Expenses

4. Discounts and sale prices

To calculate the discount:

Discount = (percentage ÷ 100) × original price

Sale price = original price − discount

Example: 20% off $50 ⇒ discount = 0.2 × 50 = $10 ⇒ sale price = $40

5. Simple interest

Simple interest is calculated using the formula:

I = P × R × T

• I: Interest
• P: Principal (initial amount)
• R: Interest rate per year (as a decimal)
• T: Time in years

Total amount = P + I

Example: P = $1,000, R = 5% (0.05), T = 3 years ⇒ I = 1000 × 0.05 × 3 = $150

6. Percentage profit and loss

• Profit = Selling price − Cost price
• Loss = Cost price − Selling price
• Percentage profit = (profit ÷ cost price) × 100%
• Percentage loss = (loss ÷ cost price) × 100%

7. GST (Goods and Services Tax)

In Australia, GST is 10% and is usually included in the displayed price.

• To add GST: Multiply price by 1.10
• To remove GST: Divide the GST-inclusive price by 1.10

Example: Item costs $100 before GST ⇒ with GST = 100 × 1.10 = $110

8. Practice questions

1. A shirt originally costs $80. It is on sale for 25% off. What is the sale price?
2. Find the simple interest on $2,000 at 4% per year for 5 years.
3. Calculate the percentage profit if an item is bought for $50 and sold for $65.
4. If a service costs $220 including GST, what is the price before GST?
5. Ben earns $22 per hour. He worked 38 hours this week. What is his pay?

9. Solutions

1. Discount = 0.25 × 80 = $20 ⇒ Sale price = $60
2. I = 2000 × 0.04 × 5 = $400
3. Profit = 65 − 50 = $15 ⇒ (15 ÷ 50) × 100 = 30%
4. 220 ÷ 1.10 = $200
5. 22 × 38 = $836