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Australia
Year 9

7.02 Income

Lesson

Introduction

When earning money, there are a few things we need to keep track of in order to know how much money we have in the present and how much we will have in the future. While they may seem like complicated, adult-only topics, things like wages, income and tax are all quite simple in terms of mathematics.

Calculate the income

Income is the technical term describing how much money is earned. When finding out how much money will be earned from a standard job, there are two main forms that information can take.

A wage is a rate of money earned per time period, usually hourly. The total amount earned is determined by how many time periods you end up working.

Conversely, a salary is a set amount that is earned over a given time period. Since the total amount earned by a salary is fixed, you can calculate an equivalent wage based on how much time you work for.

In addition to wages and salaries, income can also be affected by bonuses or rate increases for working overtime. For example, 'double time' means that the usual wage rate is doubled.

Using these types of information and calculations, we can find a person's yearly income, which is also referred to as gross annual income. This value is important for when we want to start calculating tax.

Examples

Example 1

Derek is considering three different job offers, and wants to choose the one that will pay him the most, but they are all given at different rates:

  • Offer 1: \$2917.00 per month

  • Offer 2: \$955.73 per week

  • Offer 3: \$52\,170.00 per year

a

Find his annual income for job Offer 1 at \$2917.00 per month.

Worked Solution
Create a strategy

Multiply the monthly wage by 12.

Apply the idea
\displaystyle \text{Salary}\displaystyle =\displaystyle 2917 \times 12Multiply monthly wage by 12
\displaystyle =\displaystyle \$ 35\,004Evaluate
b

Find his annual income for job Offer 2 at \$955.73 per week.

Worked Solution
Create a strategy

Multiply the weekly wage by 52.

Apply the idea
\displaystyle \text{Salary}\displaystyle =\displaystyle 955.73 \times 52Multiply weekly wage by 52
\displaystyle =\displaystyle \$ 49\,697.96Evaluate
c

Which job offer should Derek accept?

Worked Solution
Create a strategy

Compare the three annual salaries and choose which offered the most.

Apply the idea
  • Offer 1: \$35\,004.00\text{ per year}

  • Offer 2: \$49\,697.96\text{ per year}

  • Offer 3: \$52\,170.00\text{ per year}

The highest offer is Offer 3, so Derek should choose this one.

Idea summary

To convert an hourly wage to a weekly wage, multiply by the number of hours worked.

To convert a weekly wage to an annual salary, multiply the wage by 52.

To convert a monthly wage to an annual salary, multiply the wage by 12.

Taxable income and tax deductions

Taxable income is the amount of money earned in a year that the government uses to calculate tax. This amount represents the amount of money earned that a person can spend freely.

The money earned that is not spent freely can be referred to as tax deductions. Tax deductions include work related expenses and donations.

Taxable income can be calculated by subtracting tax deductions from the gross annual income.

\text{Taxable income} = \text{Gross annual income} - \text{Tax deductions}

There are different kinds of tax that need to be paid for different purposes.

Income tax is a public services tax that is calculated based on one's taxable income, in accordance with the different tax brackets.

Income tax in Australia is currently calculated according to the table below:

Taxable incomeTax on this income
0 - \$18,200\text{Nil}
\$18,201 - \$37\,00019c\text{ for each } \$1 \text{ over } \$18\,200
\$37\,001 - \$90\,000\$3572\text{ plus } 32.5c \text{ for each } \$1 \text{ over } \$37\,000
\$90\,001 - \$180\,000\$20\,797\text{ plus } 37c \text{ for each } \$1 \text{ over } \$90\,000
\$180\,001 \text{ and over }\$54\,097\text{ plus } 45c \text{ for each } \$1 \text{ over } \$180\,000

The medicare levy is a health services tax that is calculated as a flat percentage of one's taxable income. In Australia, this tax is currently equal to 2\% of one's taxable income. \\ \text{Medicare levy}=\text{Taxable income} \times 2\%

GST is the goods and services tax paid on products like toys, electronics and furniture. GST in Australia is calculated as 10\% of the product's original price. GST does not apply to food.

Since GST is added to the original price, we can calculate the sale price of items including GST using the formula: \text{Sale price}=\text{Original price}\times 1.1

Examples

Example 2

Frank works as a chef. Because he wears a uniform for his job, he is able to claim the cost and cleaning of his uniform as an allowable tax deduction.

Frank’s work-specific uniform expenses are shown in the table below.

Uniform itemNumber of itemsPrice per item ($)
\text{Chef's checked trousers}220.50
\text{Chef's jacket}125.00
\text{Chef's hat}17.85
\text{Apron}123.50
\text{Protective shoes (pair)}170.00
a

For his uniform, Frank's total cleaning expenses for the year come to \$52. Calculate Frank’s total clothing and cleaning expenses for the year.

Worked Solution
Create a strategy

Multiply the price per item by the number of items for each row, and then add the results together.

Apply the idea
\displaystyle \text{Expenses}\displaystyle =\displaystyle (2\times 20.50) + (1\times 25) + (1\times 7.85) + (1\times 23.50) + (1\times 70) + 52
\displaystyle =\displaystyle \$219.35
b

Frank also spent \$295 on a set of knives and \$15.75 on a knife pouch. He can claim these as a tools and equipment expense because he uses them only for work. Calculate his total tools and equipment expenses.

Worked Solution
Create a strategy

Add the amount spent on the knives and pouch.

Apply the idea
\displaystyle \text{Tools and equipment expenses}\displaystyle =\displaystyle 295 + 15.75Add the prices
\displaystyle =\displaystyle \$310.75Evaluate the sum
c

Calculate Frank's total allowable tax deductions.

Worked Solution
Create a strategy

Add all the expenses in part (a) and part (b).

Apply the idea
\displaystyle \text{Tax deductions}\displaystyle =\displaystyle 219.35+310.75Add all the expenses
\displaystyle =\displaystyle \$530.10Evaluate the sum
d

Frank earns \$17.50 per hour and works 40 hours per week. Calculate his annual gross income if he works 46 weeks in a year.

Worked Solution
Create a strategy

Multiply the rate per hour, the number of worked hours per week, and the number of weeks worked.

Apply the idea
\displaystyle \text{Annual gross income}\displaystyle =\displaystyle 17.50 \times 40 \times 46Multiply the values
\displaystyle =\displaystyle \$32\,200Evaluate
e

Calculate Frank's taxable income.

Worked Solution
Create a strategy

Subtract the total allowable tax deductions in part (c) from the gross income in part (d).

Apply the idea
\displaystyle \text{Taxable income}\displaystyle =\displaystyle 32\,200 - 530.10Subtract the deductions from the income
\displaystyle =\displaystyle \$31\,669.90Evaluate

Example 3

Last financial year, Roxanne earned \$154\,872.

Using the income tax rates shown in the table, evaluate the following.

Taxable incomeTax on this income
0 - \$18\,200\text{Nil}
\$18\,201 - \$37\,00019\text{c}\text{ for each } \$1 \text{ over } \$18\,200
\$37\,001 - \$87\,000\$3572\text{ plus } 32.5\text{c} \text{ for each } \$1 \text{ over } \$37\,000
\$87\,001 - \$180\,000\$19\,822\text{ plus } 37\text{c} \text{ for each } \$1 \text{ over } \$87\,000
\$180\,001 \text{ and over }\$54\,232\text{ plus } 45\text{c} \text{ for each } \$1 \text{ over } \$180\,000
a

Calculate the income tax payable on Roxanne's income.

Worked Solution
Create a strategy

We can use the income tax table.

Apply the idea

\$154\,872 lies in the range of income of \$87\,001 - \$180\,000. So, Roxanne needs to pay \$19\, 822 plus an additional amount. We can find the additional amount by subtracting \$87\,000 from \$154\,872 and multiplying the difference by 0.37.

\displaystyle \text{Tax}\displaystyle =\displaystyle 19\,822 + (154\,872 - 87\,000)\times 0.37Find the tax
\displaystyle =\displaystyle 19\,822 + 67\,872 \times 0.37Evaluate the subtraction
\displaystyle =\displaystyle 19\,822 + 25\,112.64Evaluate the multiplication
\displaystyle =\displaystyle \$44\,934.64Evaluate the addition
b

Calculate the Medicare levy payable, given that it is 2\% of taxable income.

Worked Solution
Create a strategy

We can use the formula: \text{Medicare levy}=\text{Taxable income} \times 2\%

Apply the idea
\displaystyle \text{Medicare levy}\displaystyle =\displaystyle 154\,872 \times 2\%Multiply the taxable income nu 2\%
\displaystyle =\displaystyle 154\,872 \times 0.02Convert the percentage to a decimal
\displaystyle =\displaystyle \$3097.44Evaluate
c

Calculate the total amount Roxanne needs to pay in income tax and Medicare levy.

Worked Solution
Apply the idea
\displaystyle \text{Total amount payable}\displaystyle =\displaystyle 44\,934.64 + 3097.44Add the income tax and medicare levy
\displaystyle =\displaystyle \$48\,032.08Evaluate

Example 4

The sales price of an item, including GST, is \$45. Find the price of the item without GST.

Worked Solution
Create a strategy

We can use the formula: \text{Sale Price} = \text{Original Price} \times 1.1, but since we are looking for the original price we can rearrange the equation by giving us: \text{Original price}= \dfrac{\text{Sale price}}{1.1}

Apply the idea
\displaystyle \text{Original price}\displaystyle =\displaystyle \dfrac{45}{1.1}Substitute the sale price
\displaystyle =\displaystyle \$40.91Evaluate and round
Idea summary

\text{Taxable income} = \text{Gross annual income} - \text{Tax deductions}

\text{Medicare levy}=\text{Taxable income} \times 2\%

Since GST is added to the original price, we can calculate the sale price of items including GST using the formula: \text{Sale price}=\text{Original price}\times 1.1

Income tax in Australia is currently calculated according to the table below:

Taxable incomeTax on this income
0 - \$18\,200\text{Nil}
\$18\,201 - \$37\,00019\text{c}\text{ for each } \$1 \text{ over } \$18\,200
\$37\,001 - \$90\,000\$3572\text{ plus } 32.5\text{c} \text{ for each } \$1 \text{ over } \$37\,000
\$90\,001 - \$180\,000\$20\,797\text{ plus } 37\text{c} \text{ for each } \$1 \text{ over } \$90\,000
\$180\,001 \text{ and over }\$54\,097\text{ plus } 45\text{c} \text{ for each } \$1 \text{ over } \$180\,000

Outcomes

ACMNA211

Solve problems involving simple interest

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