Superannuation Modelling
By the time you retire, your superannuation could be worth millions — or it could fall short of what you need. The difference comes down to three numbers: how much goes in, how fast it grows, and how much leaks out in fees. In this lesson you'll build a mathematical model of superannuation that reveals why starting early, choosing low fees, and maximising contributions are the most powerful financial decisions you will ever make.
Practise this lesson
Three printable worksheets that build from foundations to mastery — or build your own from any module’s questions.
Two friends start work at age 25:
Friend A: Salary $70,000 · Super contribution 11.5% · Fund return 7% p.a. · Fees 1.5% p.a.
Friend B: Salary $70,000 · Super contribution 11.5% · Fund return 7% p.a. · Fees 0.5% p.a.
They both work until 65. Without calculating — will Friend B's lower fee make a small, medium, or massive difference at retirement? Explain why.
Superannuation is an investment with three moving parts: money in (contributions), money out (fees), and growth (investment returns). The recurrence relation from Lesson 11 still applies — we just adjust the interest rate to account for fees.
Fees reduce the effective growth rate every year. The net return is what actually works for you after fees are deducted:
Then the super balance follows the same recurrence, using $r_{\text{net}}$ instead of the gross return.
Key facts
- The superannuation recurrence relation with net return
- How to calculate annual contributions from salary
- Current compulsory super rate (12% from 1 July 2025)
Concepts
- Why fees compound to massive differences over decades
- The trade-off between investment return and risk
- How salary growth changes the model
Skills
- Calculate super projections including fees
- Compare funds using net return
- Evaluate the dollar cost of fee differences over time
- Model multi-year super growth using recurrence or closed form
Everything from Lesson 11 applies. The only addition is that we must subtract fees from the return before using the recurrence formula. Let's work through a complete example:
Example: Salary = $80,000, contribution rate = 11.5%, gross return = 7%, fees = 1.2%, $A_0 = \$20{,}000$, 35 years to retirement.
The compound growth component ($814k) dwarfs the total contributions ($322k) by nearly 3:1.
Super recurrence: $A_{n+1} = (1 + r_{\text{net}})A_n + C$ where $C = \text{salary} \times \text{contribution rate}$; Net return: $r_{\text{net}} = r_{\text{return}} - r_{\text{fees}}$ — always subtract fees before calculating
Pause — copy the super recurrence $A_{n+1} = (1+r_{\text{net}})A_n + C$ where $C = \text{salary} \times \text{contribution rate}$ and $r_{\text{net}} = r_{\text{return}} - r_{\text{fees}}$ — always subtract fees before calculating — into your book.
Did you get this? True or false: if a super fund earns 7% p.a. but charges 1.5% in fees, the net return used in the recurrence relation is 5.5%.
Worked examples · 3 in a row, reveal as you go
A 30-year-old has $\$25{,}000$ in super. Salary $\$75{,}000$. Employer contributes 11.5%. Fund return 6.8% p.a. Fees 1.1% p.a. Find the projected balance at age 65.
$r_{\text{net}} = 0.068 - 0.011 = 0.057$ (5.7%)
$n = 65 - 30 = 35 \text{ years}$
$= 25{,}000(7.040) + 8{,}625(105.96) = 176{,}000 + 913{,}905 = \mathbf{\$1{,}089{,}905}$
Same person as Problem 1 ($A_0 = \$25{,}000$, salary $\$75{,}000$, 11.5% contribution, return 6.8%, 35 years). How much does switching to a 0.3% fee fund save versus the 1.1% fund?
$A_{35} = 25{,}000(1.065)^{35} + 8{,}625 \times \dfrac{(1.065)^{35} - 1}{0.065}$
$= 25{,}000(8.946) + 8{,}625(122.25) = 223{,}650 + 1{,}054{,}406 = \mathbf{\$1{,}278{,}056}$
$A_0 = \$20{,}000$, $r_{\text{net}} = 0.058$, $C = \$9{,}200$ p.a. Show the first 3 years using recurrence.
$A_2 = 1.058(30{,}360) + 9{,}200 = 32{,}121 + 9{,}200 = \$41{,}321$
$A_3 = 1.058(41{,}321) + 9{,}200 = 43{,}718 + 9{,}200 = \$52{,}918$
Quick check: A super fund earns 7% but charges 1.5% p.a. in fees. What net return should be used in the recurrence relation?
The hidden cost of fees · why 1% matters so much
We just saw the super recurrence $A_{n+1} = (1+r_{\text{net}})A_n + C$ where $r_{\text{net}} = r_{\text{return}} - r_{\text{fees}}$. That raises a question: changing fees by 0.5% seems small — but how much does it actually cost in retirement dollars over 35 years of compounding? This card answers it → the fee impact table shows that moving from 0.5% to 2.0% fees can reduce the final balance by over $600,000 because every dollar lost to fees is a dollar that cannot compound for decades.
A 1% fee sounds trivial. Over 40 years it can cost you hundreds of thousands of dollars because fees compound just like returns — but against you. Based on $A_0 = \$20{,}000$, salary $\$80{,}000$, 11.5% contribution, gross return 7%, 35 years:
| Fee rate | Net return | Balance at 65 | Difference |
|---|---|---|---|
| 0.5% | 6.5% | $1,450,000 | — |
| 1.0% | 6.0% | $1,210,000 | −$240,000 |
| 1.5% | 5.5% | $1,010,000 | −$440,000 |
| 2.0% | 5.0% | $845,000 | −$605,000 |
The difference between 0.5% and 2.0% fees is over $\$600{,}000$ — more than the total contributions of many workers. Fees are the silent killer of retirement wealth.
Fees are charged annually as a % of balance — so every dollar in fees is a dollar that cannot compound; A 1% extra fee does not cost 1% of final balance — it costs much more because the lost dollars would...
Pause — copy the fee-compounding insight: fees are charged as a % of the balance each year, so every dollar in fees is a dollar that can no longer compound — a 1% extra fee costs far more than 1% of the final balance — into your book.
Think through this: A worker contributes $9,200 per year for 35 years (total contributions = $322,000). If their final balance is $1,137,000, what percentage of the balance came from compound growth, not contributions?
Quick-fire practice · 5 super calculations
Salary $\$60{,}000$, contribution rate 11.5%. What is $C$?
Gross return 7.5%, fees 1.2%. What is $r_{\text{net}}$?
Write the recurrence relation: $A_0 = \$15{,}000$, $r_{\text{net}} = 5.8\%$, $C = \$8{,}625$ p.a.
From the fee table, how much does switching from 1.5% to 0.5% fees save over 35 years?
$A_0 = \$15{,}000$, $r_{\text{net}} = 0.062$, $C = \$6{,}900$ p.a. Find $A_1$.
Fill in the blanks: In superannuation modelling, the net return is calculated as $r_{\text{net}}$ = gross return [blank]. The annual contribution is salary [blank]. A higher fee rate means a [blank] net return, resulting in a smaller retirement balance.
Match each scenario to its description:
- Higher gross return
- Higher fee rate
- Higher salary
- Longer time horizon
- Increases $n$ — more periods of compounding
- Increases contribution $C$ — more goes in each year
- Decreases $r_{\text{net}}$ — reduces final balance
- Increases $r_{\text{net}}$ — grows balance faster
Earlier you predicted whether the fee difference would be small, medium, or massive. The answer: massive.
Friend B (0.5% fees, net return 6.5%) retires with approximately $1.45 million. Friend A (1.5% fees, net return 5.5%) retires with approximately $1.01 million. The fee difference of just 1% costs Friend A $440,000 — enough to buy a house in many parts of Australia. This happens because fees reduce the net return from 5.5% to 6.5%, and that 1% gap compounds every year for 40 years. The effect is exponential, not linear. Over a lifetime, fees are often the single largest determinant of retirement wealth after the contribution rate itself.
Pick your answer, then rate your confidence — that tells the system what to drill next. Each retry pulls a fresh mix from the bank.
Q1. Salary $\$85{,}000$, contribution rate 11.5%, gross return 7%, fees 1.2%, $A_0 = \$30{,}000$, $n = 30$ years. (a) Find $r_{\text{net}}$ and $C$. (b) Calculate $A_{30}$ using the closed-form formula. (3 marks)
Q2. Two funds offer identical conditions ($A_0 = \$20{,}000$, salary $\$80{,}000$, 11.5% contribution, gross return 7%, 25 years) except fees: Fund A charges 1%, Fund B charges 0.5%. (a) Calculate the net return for each fund. (b) Find the difference in projected balances. (3 marks)
Q3. $A_0 = \$20{,}000$, salary $\$80{,}000$, 11.5% contribution, net return 5.8%. (a) Write the recurrence relation. (b) Find $A_1$ and $A_2$. (c) Using the closed form, verify $A_2$. Explain any small difference. (4 marks)
Comprehensive answers (click to reveal)
Drill 1: $C = 60{,}000 \times 0.115 = \$6{,}900$ p.a.
Drill 2: $r_{\text{net}} = 7.5\% - 1.2\% = 6.3\% = 0.063$
Drill 3: $A_{n+1} = 1.058 A_n + 8{,}625$, $A_0 = 15{,}000$
Drill 4: From the table: $\$1{,}450{,}000 - \$1{,}010{,}000 = \$440{,}000$ saved
Drill 5: $A_1 = 1.062(15{,}000) + 6{,}900 = 15{,}930 + 6{,}900 = \$22{,}830$
Q1 (3 marks): (a) $r_{\text{net}} = 7\% - 1.2\% = 5.8\%$ [1]; $C = 85{,}000 \times 0.115 = \$9{,}775$ p.a. [1]. (b) $A_{30} = 30{,}000(1.058)^{30} + 9{,}775 \times [(1.058)^{30}-1]/0.058 = 30{,}000(5.31) + 9{,}775(74.3) = 159{,}300 + 726{,}293 = \$885{,}593$ [1].
Q2 (3 marks): (a) Fund A: $r_{\text{net}} = 6\%$; Fund B: $r_{\text{net}} = 6.5\%$ [1]. (b) $C = 80{,}000 \times 0.115 = \$9{,}200$. Fund A: $A_{25} = 20{,}000(1.06)^{25} + 9{,}200 \times [(1.06)^{25}-1]/0.06 \approx \$549{,}000$. Fund B: $A_{25} \approx \$616{,}000$. Difference $\approx \$67{,}000$ [2].
Q3 (4 marks): (a) $A_{n+1} = 1.058 A_n + 9{,}200$, $A_0 = 20{,}000$ [1]. (b) $A_1 = 1.058(20{,}000)+9{,}200 = \$30{,}360$; $A_2 = 1.058(30{,}360)+9{,}200 = \$41{,}321$ [2]. (c) Closed form: $A_2 = 20{,}000(1.058)^2 + 9{,}200 \times [(1.058)^2-1]/0.058 = 22{,}393 + 18{,}936 = \$41{,}329$. Small difference due to rounding intermediate recurrence steps — both methods are equivalent [1].
Five timed questions. Beat the boss to bank a tier — gold (90% + speed), silver (75%), or bronze (50%). Replays welcome.
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