Financial Mathematics A: Earning, Saving and Spending Money Stage 5 · Year 10 · Unit of Work

Unit plan and overview

Unit Class Length
Financial mathematics A (Stage 5) Year 10, middle ability set 9 lessons of 60 minutes, plus 1 outline lesson
Threads that run through the unit

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Financial mathematics AStage 5 · MA5-FIN-C-01 and MAO-WM-01Year 10 middle ability set · 9 lessons of 60 minutes + 1 outline
Earn itWhich job pays the most?

1Ways of earning money

  • Wage = hourly rate × hours. Salary = a set amount per year
  • Commission and royalties are a % of sales. Piecework is pay per item
  • ICT diagnostic quiz checks %, decimals, time and tables
  • 5% written as 0.5. Commission worked out on the retainer

2Overtime and penalty rates

  • Pay = base rate × multiplier × hours
  • Time and a half × 1.5, double time × 2
  • Overtime rate changes after 2 hours (real Fair Work pay guide)
  • Adding 1.5 instead of multiplying. Adding the hours

3Gross to take-home pay

  • 1 year = 52 weeks, so a month is 52 ÷ 12 ≈ 4.33 weeks
  • Leave loading: 17.5% of 4 weeks' pay. Casuals get no paid leave
  • Net pay = gross pay − tax withheld (ATO tax table)
  • Monthly pay = 4 × weekly pay. Adding the tax

3bTaxable income (outline)

  • Income − allowable deductions, 2026–27 resident tax rates
Grow itHow does money grow over time?

4Developing the formula

  • Equal yearly interest on the original principal builds the rule
  • I = Prn and A = P + I
  • Months ÷ 12 = years when the rate is per annum
  • 18 months = 1.8 years. Interest mixed up with total amount

5Applying the formula

  • Find a missing rate or time, then check by substitution
  • First amount graph by hand: rule → table → points
  • r = 0.015 read as 0.015%. Amount graph starting at zero

6Tables and graphs

  • Initial value = principal. Gradient = interest per year (Pr)
  • ICT spreadsheet: change the rate to 4%, 6% or 8%
  • AoL independent checkpoint (8 marks)
  • Gradient read as the total rise or as a percentage
Spend or borrow itWhat does it really cost?

7Paying over time

  • Opens by contrasting L6 simple interest with a plan's extra cost
  • Total paid = deposit + all repayments
  • Extra cost = total paid − cash price
  • AoL exit ticket (4 marks)
  • A smaller monthly payment means it is cheaper

8Buy now, pay later

  • Payment schedule includes the payment made today
  • Account charges and late fees, not interest
  • ICT spreadsheet model checked against hand working
  • AoL exit ticket (4 marks)
  • 'Interest-free' means it costs nothing extra

9Short-term loans

  • Total repaid = principal + fees
  • Borrowing cost = total repaid − principal
  • ICT duration model. AoL spending assessment (17 marks)
  • Closing case: earnings, simple interest and the choice to wait or borrow
  • Fee worked out on the wrong amount

formula ⚠ common misconception ▸ technology or assessment · Click a lesson card to open that lesson.

How the unit flows

The unit follows money in the order students meet it. They earn it (Lessons 1–3), let it grow (Lessons 4–6), then spend or borrow it (Lessons 7–9). Each part has one driving question, and its lessons build towards answering it. Lesson 9 closes the unit with a case that brings the three parts together: a weekly surplus from earnings, savings grown by simple interest, and the choice between waiting and borrowing.

Part Driving question Progression
Earning money (Lessons 1–3) Which job pays the most? Name the ways of being paid → calculate extra pay → compare jobs over the same period and find take-home pay
Simple interest (Lessons 4–6) How does money grow over time? Build I = Prn from equal yearly interest → find a missing rate or time and draw the first amount graph → read the initial value and gradient, and compare rates in a spreadsheet
Spending money (Lessons 7–9) What does it really cost? Deposit and repayments → extra charges and conditions → comparing borrowing costs → closing case across the unit

Lessons

Lesson Title Key ideas
1 Ways of Earning Money Unit introduction and diagnostic quiz. Wage, salary, commission, piecework and royalties
2 Overtime, Weekend and Public Holiday Pay Pay = base rate × multiplier × hours. Overtime that changes rate after 2 hours, using a real award pay guide
3 From Gross Pay to Take-Home Pay Weekly, fortnightly, monthly and yearly pay (1 year = 52 weeks). Leave loading. ATO weekly tax table. Net pay
3b Taxable Income (outline only) Allowable deductions, 2026–27 resident tax rates, tax payable for the year
4 Developing the Simple Interest Formula I = Prn built from equal yearly interest. A = P + I. Months to years. Finding and explaining errors
5 Applying the Simple Interest Formula Finding a missing rate or time and checking by substitution. Values table and first amount graph. Finding the principal as an extension
6 Representing Simple Interest with Tables and Graphs Initial value and gradient. Changing the rate in a spreadsheet. Matching rule, table and graph. Independent checkpoint (8 marks)
7 Paying for a Purchase Over Time Opening link to Lesson 6 simple interest. Percentage deposits and payment counts. Total paid and extra cost above the cash price. Comparing plans of different lengths
8 Buy Now, Pay Later: What Does It Really Cost? Payment schedules, account charges and late fees. Checking a spreadsheet model against hand working
9 Short-term Small Loans: Comparing Borrowing Costs Fees on the amount borrowed, total repaid and borrowing cost. Comparing loans. Independent spending assessment (17 marks), ending with a closing case on earning, simple interest and spending

How the unit connects to the rest of the syllabus

The unit builds on percentage, algebra and equation work from Stage 4 and leads into compound interest and senior financial mathematics.

Builds on

Stage 3 Additive relations BMA3-AR-01Adding and subtracting money: total pay, total paid (Lessons 1–3, 7–9)
Stage 4 Fractions, decimals and percentagesMA4-FRC-C-01Commission (Lesson 1), leave loading (Lesson 3), interest rates (Lessons 4–6), deposits and fees (Lessons 7, 9)
Stage 4 Algebraic techniquesMA4-ALG-C-01Substituting into pay = base rate × multiplier × hours (Lesson 2) and I = Prn (Lessons 4–6)
Stage 4 EquationsMA4-EQU-C-01Finding a missing rate or time from I = Prn (Lesson 5)
Stage 4 Data classification and visualisationMA4-DAT-C-01Reading the ATO tax table (Lesson 3) and payment schedules (Lesson 8)
Stage 5 Financial mathematics AMA5-FIN-C-01solves financial problems involving simple interest, earning money and spending money

Alongside in Stage 5

Stage 5 Linear relationships BMA5-LIN-C-02A simple interest graph is a straight line; its gradient is the interest earned per year (Lesson 6)

Leads to

Stage 5 Financial mathematics BMA5-FIN-C-02Compound interest and depreciation, after simple interest (Lessons 4–6)*
Stage 6 Mathematics StandardTaxable income, explored further in the taxation section (Lesson 3 and outline Lesson 3b)
Stage 6 Mathematics AdvancedLoan repayments and financial applications of series (Lessons 7, 9)
Stage 6 Numeracy CEC 3.3.2, 3.3.3Spreadsheets for wages, PAYG tax and net earnings, and for budgets (Lessons 8, 9)

Across the curriculum

Aboriginal and Torres Strait Islander histories and culturesCommission on artworks (Lesson 1 extension)
Stage 4 GeographyIncome and employment as factors in how people see liveability
Stage 5 Technological and Applied Studies, Stage 4 TechnologyPlanning the production cost of a design

The connections are the ones the NSW Education Standards Authority lists for Financial mathematics A (NSW Education Standards Authority [NESA], 2022a, Financial mathematics A teaching advice), except *Financial mathematics B, which is the next Stage 5 focus area. Outcome codes are from NESA (2022a). The lesson links in brackets are ours.

References