Superannuation as an annuity: 12 per cent super guarantee over a working life

The idea

Equal contributions that each earn compound interest add to a geometric series, so the future value of an annuity has a closed form and grows much faster than the sum of the contributions.

What you need

• The ATO super guarantee table: 12.00 per cent of earnings from 1 July 2025
• A spreadsheet, and a table of future value interest factors

How to do it

1. For a test salary of $70 000 a year, compute the yearly super guarantee contribution at 12 per cent.
2. Model the account in a table for the first four years at an assumed 5 per cent a year, with each contribution added at the end of the year.
3. Show that the future value after n years is the geometric series C (1 + (1.05) + (1.05)^2 + ... + (1.05)^(n-1)) = C ((1.05)^n - 1)/0.05.
4. Compute the future value after 40 years and the total of the contributions.
5. Vary the return (3, 5 and 7 per cent) and the starting age and describe the effect of each.

What you should see

12 per cent of $70 000 is $8400 a year. At 5 per cent the balances at the end of years 1 to 4 are $8400.00, $17 220.00, $26 481.00 and $36 205.05. The 40-year future value interest factor is 120.79977 (120.7998 to four decimal places), so the account reaches $1 014 718.10 from contributions totalling $336 000; interest supplies about two thirds of the final value. This model omits contributions tax, fees and salary growth, and the 5 per cent return is an assumption, not a forecast. The learner knows it worked when the spreadsheet's year-40 balance is $1 014 718.10, the value of C ((1.05)^40 - 1) / 0.05 kept at full precision; the factor rounded to 120.7998 returns $1 014 718.32, so a check to the cent cannot use the rounded factor.

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.

• The final balance is roughly the sum of the contributions; here interest supplies about two thirds of it.
• Starting ten years later loses a quarter of the balance; with 30 years instead of 40 the model gives $558 086.32, about 45 per cent less, because the early contributions compound longest.

Safety card

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 2 focus area Annuities; 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-S2-03
• Mathematics Advanced 11–12 Syllabus (2024), Year 12 focus area Financial mathematics; 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-12-08
• 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.

1. curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/year-12-tba2/faa14f8aa3
2. curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-advanced-11-12-2024/content/year-12/fa4572a048
3. curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-advanced-11-12-2024/content/year-12/fa8db67617
4. www.ato.gov.au/tax-rates-and-codes/key-superannuation-rates-and-thresholds/super-guarantee
5. amsi.org.au/ESA_Senior_Years/SeniorTopic1/1d/1d_1intro.html