Earning Money — NSW Year 10 Advanced Maths
Wages, income tax, interest, buying on terms and depreciation, the maths of everyday money. Six subtopics and 120 practice questions, each with a fully worked solution, aligned to NESA outcomes MA5-FIN-C-01 and MA5-FIN-C-02.
Earning Money in NSW Year 10 Advanced
Earning Money is financial mathematics for real decisions: how pay is calculated, how much income tax is owed, how savings grow, what buying on terms really costs, and how fast a new car loses value. Year 10 Advanced students use formulas such as \(I=Prn\) and \(FV=PV(1+r)^n\), rearrange them to find unknowns, and compare options.
The six subtopics below start with earning an income and income tax, then cover simple interest, compound interest and term payments, and finish with depreciation. Earning Money is one of the 16 topics in NSW Year 10 Advanced Maths and sits within the Number and Algebra strand (NESA outcomes MA5‑FIN‑C‑01 and MA5‑FIN‑C‑02). The same ideas lead to financial mathematics in Year 11 and 12, including annuities and loan repayments.
Subtopics
Earning Money: common questions
What is the difference between simple and compound interest?
Simple interest is paid only on the original amount, so it is the same each year: \(I=Prn\). Compound interest is also paid on interest already earned, so it grows faster: \(FV=PV(1+r)^n\). For example, $50 000 at 8% p.a. for 5 years earns $20 000 simple interest but about $24 297 compounded quarterly.
How do you calculate overtime pay?
Multiply the extra hours by the hourly rate and by the overtime rate. At $24.60 an hour, 5 hours at time-and-a-half is \(5\times1.5\times24.60=\$184.50\) and 3 hours at double time is \(3\times2\times24.60=\$147.60\).
What is taxable income?
Taxable income is all your income, including wages and bank interest, minus allowable deductions such as work uniforms or union fees. Income tax is then worked out from the tax table, and the Medicare levy is usually 2% of taxable income.
How do you calculate depreciation?
Use \(S=V_0(1-r)^n\). A smart watch that costs $1200 and loses 18% of its value each year is worth \(1200\times0.82^3\approx\$661.64\) after 3 years.
Which NESA outcomes cover Earning Money?
Earning an income, income tax, simple interest and buying on terms are MA5‑FIN‑C‑01, and compound interest and depreciation are MA5‑FIN‑C‑02. Both are Core outcomes in Stage 5 of the NSW Mathematics K–10 Syllabus (2022).