Mathematics 11–12 · Year 12

Simple and compound interest at a real savings rate from the Reserve Bank

Investment (Mathematics Standard 1, Year 12); Investment and loans: Investment (Mathematics Standard 2, Year 12); Sequences and series: Geometric sequences and series (Mathematics Advanced, Year 12)

Calculation and dataLow risk

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The idea

Compound interest adds interest to the balance each period, so the balance grows geometrically, and compounding more often at the same annual rate adds slightly more each time.

What you need

RBA statistical table F4 (retail deposit and investment rates): online savings accounts, $10 000, 3.10 per cent a year in August 2026 (series FRDIRSAO10K)
RBA cash rate target: 4.35 per cent since 6 May 2026 (unchanged at the 12 August 2026 decision)
The Moneysmart compound interest calculator for checking, and a spreadsheet

How to do it

Look up the latest online savings rate in RBA table F4 and the current cash rate target, and record both with their dates.
For $10 000 over 5 years at 3.10 per cent a year, compute the simple interest with I = Prn.
Compute the future value with FV = PV (1 + r)^n for yearly, monthly and daily compounding (r and n per period).
Build a spreadsheet of the monthly balances and show that successive balances form a geometric sequence; state its common ratio.
Graph simple and compound balances over 30 years and describe the shapes; find the doubling time.
Check one answer with the Moneysmart calculator.

What you should see

At 3.10 per cent a year for 5 years, $10 000 earns $1550.00 simple interest ($11 550.00 in total); compounded yearly it grows to $11 649.13, monthly to $11 674.25 and daily to $11 676.50. The monthly balances form a geometric sequence with common ratio 1 + 0.031/12 = 1.002583, and the money doubles in 22.4 years with monthly compounding. The simple-interest graph is a straight line and the compound graph an exponential curve that pulls away from it. The learner knows it worked when the spreadsheet's month-60 balance equals the formula value to the cent and matches the Moneysmart calculator.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Compound interest at 3.1 per cent for 5 years is 15.5 per cent; compounding makes it 16.7 per cent when monthly.
Compounding daily instead of monthly makes a large difference; at 3.1 per cent it adds $2.25 on $10 000 over 5 years.

Safety card

Low riskLearners carry it out

Hazards

No hazard is listed.

Controls

No control is listed.

Note

No chemicals and no heat: the NSW Department of Education Chemical Safety in Schools package does not apply. The activity uses published rates and stated test amounts only; no learner's or family's own financial details are needed.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 1 focus area Investment; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S1-02
Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 2 focus area Investment and loans; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S2-02
Mathematics Advanced 11–12 Syllabus (2024), Year 12 focus area Sequences and series; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MAV-12-03
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

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