Interest and Depreciation (HSC SSCE Mathematics Standard): Revision Notes

Calculating GST

What is GST?

When you buy goods or services in Australia, the government adds a tax to your purchase. This tax is called GST, which stands for Goods and Services Tax. The GST rate in Australia is set at 10% of the pre-tax price.

Most purchases include GST, but there are some exceptions. Basic food items and certain medical expenses are typically exempt from GST. This means you won't pay the extra 10% tax on these essential items.

Calculating GST: three essential methods

There are three main types of GST calculations you need to master. Each one helps you answer a different question about prices and tax.

Method 1: Finding the GST amount

To work out how much GST you'll pay on an item, multiply the pre-tax price by 10% (or 0.10).

$\text{GST} = 0.10 \times \text{pre-tax price}$

Method 2: Finding the total cost including GST

You can find the total cost in two ways:

Way 1: Add the GST amount to the pre-tax price.

$\text{Total cost} = \text{pre-tax price} + \text{GST}$

Way 2: Multiply the pre-tax price by 110% (or 1.10). This works because $100\% + 10\% = 110\%$.

$\text{Total cost} = 1.10 \times \text{pre-tax price}$

Method 3: Finding the pre-tax price from the total cost

Sometimes you know the final price (including GST) and need to work backwards to find what the item cost before tax was added. To do this, divide the total cost by 110% (or 1.10).

$\text{Pre-tax price} = \text{Total cost} \div 1.10$

Worked example: concert ticket with GST

International comparison: VAT

In many countries around the world, the equivalent of GST is called VAT, which stands for Value Added Tax. While the principle is the same as GST, the tax rate varies significantly between countries. VAT rates can range anywhere from 2% to 25%, depending on the country and type of goods or services.

The calculations for VAT work in exactly the same way as GST calculations. The only difference is that you use the specific VAT rate for that country instead of Australia's 10% GST rate.

VAT calculation formulas

The formulas for VAT calculations follow the same pattern as GST:

Finding the VAT amount:

$\text{VAT} = \text{VAT rate} \times \text{pre-tax price}$

Finding the total cost:

$\text{Total cost} = \text{pre-tax price} + \text{VAT}$

Or alternatively:

$\text{Total cost} = (100\% + \text{VAT rate}) \times \text{pre-tax price}$

Finding the pre-tax price:

$\text{Pre-tax price} = \text{Total cost} \div (100\% + \text{VAT rate})$

Worked example: microwave with VAT

Remember!