Percentage Applications
Apply percentages to real-world situations including profit and loss, GST, and simple and compound interest.
Profit and Loss
When goods are bought and sold, the difference between the selling price and the cost price determines whether a profit or loss was made.
Profit
Selling price > Cost price
Profit = Selling Price − Cost Price
Profit % = (Profit ÷ Cost Price) × 100
Loss
Selling price < Cost price
Loss = Cost Price − Selling Price
Loss % = (Loss ÷ Cost Price) × 100
GST (Goods and Services Tax)
In Australia, most goods and services include a 10% GST added to the pre-tax price. You need to be able to both add GST and find the pre-GST price.
Adding GST
Multiply the pre-tax price by 1.10
Price with GST = Price × 1.10
Removing GST
Divide the GST-inclusive price by 1.10
Pre-tax Price = Price ÷ 1.10
Simple and Compound Interest
Simple Interest
Interest is calculated on the original principal only. The interest amount stays the same each year.
I = P × R × T
P = principal, R = rate (as decimal), T = time (years)
Compound Interest
Interest is calculated on the principal plus accumulated interest. Your money grows faster over time.
A = P(1 + r)n
A = final amount, P = principal, r = rate, n = periods
Growth Comparison: $1,000 at 10% for 3 Years
Compound interest earns more because each year's interest is added to the principal.
Percentage Increase and Decrease
Multiplier Method
Use a single multiplication to apply a percentage change.
Finding Percentage Change
When you know the original and new values:
% Change = (Change ÷ Original) × 100
A positive result = increase. A negative result = decrease.
Key Vocabulary
Principal
The original amount of money invested or borrowed before interest is added.
GST
Goods and Services Tax — a 10% tax applied to most goods and services in Australia.
Simple Interest
Interest calculated on the original principal only, using I = PRT.
Compound Interest
Interest calculated on the principal plus previously earned interest, using A = P(1 + r)n.
Worked Examples
A bike costs $320. It is sold for $400. Find the profit percentage.
Step 1: Find the profit: $400 − $320 = $80
Step 2: Profit % = (80 ÷ 320) × 100 = 25%
Answer: 25% profit
A laptop is priced at $1,200 before GST. What is the price with GST included?
Step 1: GST = 10% of $1,200 = $120
Step 2: Price with GST = $1,200 × 1.10 = $1,320
Answer: $1,320
$5,000 is invested at 6% p.a. compound interest for 2 years. Find the final amount.
Step 1: Use A = P(1 + r)n where P = 5000, r = 0.06, n = 2
Step 2: A = 5000 × (1.06)2 = 5000 × 1.1236 = $5,618
Answer: $5,618
Knowledge Check
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Key Concepts Summary
- ●Profit % = (Profit ÷ Cost Price) × 100; Loss % = (Loss ÷ Cost Price) × 100.
- ●Australian GST is 10%. Add GST by multiplying by 1.10; remove it by dividing by 1.10.
- ●Simple interest: I = PRT (interest on original principal only).
- ●Compound interest: A = P(1 + r)n (interest on growing balance).
- ●Use the multiplier method for quick percentage increases and decreases.