Simple Interest

Simple interest is calculated only on the original amount (the principal). The interest earned each year stays the same.

Simple Interest Formula

I = P × R × T

I = Interest earned | P = Principal (original amount)

R = Annual interest rate (as a decimal) | T = Time (in years)

Key Point: To convert a percentage to a decimal, divide by 100. For example, 5% = 0.05.

Compound Interest

Compound interest is calculated on the principal plus any interest already earned. This means your money grows faster over time because you earn "interest on interest."

Compound Interest Formula

A = P(1 + r)ⁿ

A = Final amount | P = Principal

r = Annual interest rate (as a decimal) | n = Number of years

Simple vs Compound Interest Growth

$1,000 invested at 5% per annum. Compound interest curves upward as interest earns interest.

GST Calculations

In Australia, the Goods and Services Tax (GST) is 10% added to the price of most goods and services.

Adding GST

Price with GST = Price × 1.10

Removing GST

Price without GST = Price ÷ 1.10

Profit, Loss & Discounts

Profit

Profit = Selling Price − Cost Price. When you sell something for more than you paid, you make a profit.

Loss

Loss = Cost Price − Selling Price. When you sell something for less than you paid, you make a loss.

Percentage Profit/Loss

% Profit/Loss = (Profit or Loss ÷ Cost Price) × 100

Discount

Sale Price = Original Price × (1 − discount rate). For example, 20% off: Sale Price = Original × 0.80.

Key Vocabulary

Term	Definition
Principal (P)	The original amount of money invested or borrowed.
Interest Rate (R/r)	The percentage charged or earned per time period, usually per annum (p.a.).
Simple Interest	Interest calculated only on the original principal amount.
Compound Interest	Interest calculated on the principal plus accumulated interest.
GST	Goods and Services Tax — a 10% tax added to most Australian goods and services.
Discount	A reduction in the original selling price, usually expressed as a percentage.

Worked Examples

1

Simple Interest Calculation

Sarah invests $2,000 at 4% per annum simple interest for 3 years. How much interest does she earn?

Step 1: Identify values. P = $2,000, R = 4% = 0.04, T = 3 years

Step 2: Apply formula. I = P × R × T

Step 3: Calculate. I = 2000 × 0.04 × 3 = $240

Total after 3 years: $2,000 + $240 = $2,240

2

Compound Interest Calculation

Jake invests $5,000 at 6% per annum compound interest for 4 years. What is the final amount?

Step 1: Identify values. P = $5,000, r = 6% = 0.06, n = 4

Step 2: Apply formula. A = P(1 + r)ⁿ = 5000(1.06)⁴

Step 3: Calculate. A = 5000 × 1.2625 = $6,312.38

Interest earned: $6,312.38 − $5,000 = $1,312.38

3

Discount and GST Combined

A laptop costs $1,200 (before GST). It is on sale with a 15% discount. What is the final price including GST?

Step 1: Calculate discount. Discount = $1,200 × 0.15 = $180

Step 2: Discounted price. $1,200 − $180 = $1,020

Step 3: Add GST (10%). $1,020 × 1.10 = $1,122.00

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see feedback.

Question 1

$3,000 is invested at 5% per annum simple interest for 2 years. What is the total interest earned?

$150 $300 $600 $3,300

Question 2

$1,000 is invested at 8% compound interest for 3 years. What is the final amount? (Round to 2 d.p.)

$1,240.00 $1,080.00 $1,259.71 $1,360.49

Question 3

A pair of shoes costs $89.00 including GST. What was the price before GST?

$80.00 $97.90 $79.00 $80.91

Question 4

A shop buys a jacket for $60 and sells it for $45. What is the percentage loss?

25% 33.3% 15% 20%

Question 5

A TV originally costs $800. It is discounted by 30%. What is the sale price?

$240 $560 $600 $770

Financial Mathematics