Income and deductions
Keep earnings and deductions in the same time period. Calculate gross income first, then subtract the stated deductions. Use only the fictional tax rule supplied in the question
\[\text{Net}=\text{Gross}-\text{Deductions}\]
- Hourly pay For a block of h hours paid at rate r, multiply hours by that rate. Use one and a half times the ordinary rate for time-and-a-half, or twice the ordinary rate for double time. Add the earnings blocks \(\displaystyle \text{Earnings}=hr\)
- Salary conversion Let A be annual salary, w the paid weeks in the year and h the ordinary hours each week. An hourly rate uses all ordinary hours in the year. Round only the final requested amount \(\displaystyle \begin{aligned}\text{Weekly pay}&=\frac{A}{w}\\\text{Hourly rate}&=\frac{A}{wh}\end{aligned}\)
- Recover an ordinary rate Count time-and-a-half hours as one and a half ordinary hours and double-time hours as two. Let H be their total equivalent ordinary hours, G gross pay and r the ordinary hourly rate. Divide gross pay by H. These are pay equivalents, not extra hours worked \(\displaystyle r=\frac{G}{H}\)
- Commission and retainer Let S be sales, p the commission percentage, C the commission and R the retainer. Calculate commission on sales and add the fixed retainer for the same period \(\displaystyle \begin{aligned}C&=S\times\frac{p}{100}\\\text{Gross pay}&=R+C\end{aligned}\)
- A tax-free threshold Under a single-rate practice rule, tax is zero at or below the threshold. Above it, subtract the threshold from gross income, calculate tax on the excess, then subtract that tax from gross income
- Tax as a percentage Let T be tax and G gross income for the same period. Express their ratio as a percentage. If the question names gross income as the whole, do not divide by net income \(\displaystyle \text{Tax proportion}=\frac{T}{G}\)
- Compare arrangements Use the same period and work conditions for both arrangements. Calculate each gross amount before comparing them. A higher gross amount alone does not describe every feature of a job
Common mistakes
Adding deductions
✕\(\displaystyle \text{Net pay}=864+137=1{,}001\)✓\(\displaystyle \text{Net pay}=864-137=727\)
Deductions are taken from earningsUsing ordinary rates for overtime
✕\(\displaystyle \begin{aligned}\text{Pay}&=5\times28.40\\&=142\end{aligned}\)✓\(\displaystyle \begin{aligned}\text{Pay}&=5\times1.5\times28.40\\&=213\end{aligned}\)
For five hours at time-and-a-half with an ordinary rate of $28.40, increase the rate before calculating the payTaxing the untaxed portion
✕\(\displaystyle \begin{aligned}\text{Tax}&=0.16\times43{,}600\\&=6{,}976\end{aligned}\)✓\(\displaystyle \begin{aligned}\text{Tax}&=0.16(43{,}600-15{,}600)\\&=0.16\times28{,}000\\&=4{,}480\end{aligned}\)
Under this fictional rule, 16% tax applies only to annual income above $15,600. Gross annual income is $43,600. Subtract the untaxed threshold before calculating the taxDifficulty levels
introCalculate a wage or convert annual salary to weekly pay or an hourly rate
standardCalculate overtime earnings or a retainer with commission
challengeRecover an ordinary rate from overtime pay, or apply a tax threshold and interpret tax as a percentage of gross income
examCalculate and compare pay arrangements for the same period and work conditions
Questions about this topic
Are these Australian tax tables?+
No. Each tax question supplies a fictional rule for practising the calculation
Does a higher tax deduction mean lower net income?+
Compare the actual amounts. Under the single-rate rules used here, earning more above the threshold increases both tax and net income
When should I round a salary conversion?+
Keep the intermediate calculation exact and round only the requested final amount
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 1: Number and financial mathematics
In this chapter
Evaluate an integer expressionFactors, multiples, HCF, LCM and primesRound to decimal places or significant figuresEstimate an expression using rounded inputsConvert between fractions, mixed numbers and decimalsClassify real numbers and compare exact valuesAdd, subtract, multiply and divide fractions and mixed numbersWrite a ratio from countsWrite ratios in simplest formComplete equivalent ratiosUse a constant rateDivide a quantity in a given ratioDecide which option is the better valueConvert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1F Percentages and money: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changePercentage error against a reference value1G Percentage change and percentage error: Find the original amount from a percentageProfit, mark-up and discountIncome and taxSimple interestCompound interest (optional extension)