Mathematics 7–10 · Year 10
Compound interest as exponential growth, checked against Moneysmart
Number and algebra
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The idea
An amount that grows by a fixed percentage each period follows A = P(1 + r/n)^(nt), an exponential relationship whose graph curves upward, and the compounding frequency changes the outcome by a computable amount.
What you need
- Spreadsheet or calculator
- Access to the ASIC Moneysmart compound interest calculator for an independent check
How to do it
- Compute by hand the value of $1000 after 1, 2 and 3 years at 5 per cent per year compounded yearly, multiplying by 1.05 each time.
- Build a spreadsheet column for years 0 to 10 and plot the amount; compare the shape with simple interest at the same rate (a straight line).
- Change to monthly compounding with the formula A = P(1 + 0.05/12)^(12t) and compare the 10-year amount.
- Enter the same inputs into the Moneysmart calculator (it credits interest monthly or annually) and confirm its 10-year figure agrees with the spreadsheet to the precision the calculator displays.
- Find, by trial in the spreadsheet, how many years it takes the amount to double at 5 per cent yearly.
What you should see
$1000 at 5 per cent per year compounded yearly is $1276.28 after 5 years and $1628.89 after 10 years; monthly compounding gives $1647.01 after 10 years, $18.11 more than the yearly amount (the two amounts rounded to the cent differ by $18.12). Simple interest gives $1500 after 10 years, and the compound curve pulls away from the straight line more each year. Doubling takes between 14 and 15 years (1.05^14 = 1.980, 1.05^15 = 2.079). The learner knows it worked when the spreadsheet's 10-year yearly figure is $1628.89 and the Moneysmart calculator's figure for the same inputs agrees to the precision it displays.
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.
- Five per cent for ten years is fifty per cent in total.
- Monthly compounding doubles the interest compared with yearly.
- The amount grows by the same number of dollars each year.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
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 K–10 Syllabus (2022), Stage 5 Financial mathematics B; the page's one formula point gives FV = PV(1 + r)^n with r the interest rate per time period and n the number of time periods, which covers the yearly case and the monthly case with r per month, but neither it nor ACARA AC9M10A04, a general growth and decay modelling description, carries the comparison of compounding frequencies at one annual rate that the second half of the concept rests on; page read 2026-09-23MA5-FIN-C-02
- Australian Curriculum v9AC9M10A04AC9M10A03
Sources
The pages the author read to write this activity.