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Module 7 · L12 of 20 ~40 min ⚡ +95 XP available

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.

Today's hook, A 1% fee sounds trivial. But applied to a growing balance over 40 years, that 1% compounds against you every single year, costing the average worker over $440,000. Maths, not luck, determines retirement wealth.
0/5QUESTS

Get oriented

Recall what you already know, meet the superannuation model and settle the terms.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any module question
01
Recall, your gut answer first
+5 XP warm-up

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.

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02
Modelling superannuation
+5 XP to read

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.

Subtract fees from the gross return to get the net rate used in the recurrence.
$$r_{\text{net}} = r_{\text{return}} - r_{\text{fees}}$$
Contribution $C$
$C = \text{salary} \times \text{contribution rate}$. From 1 July 2025, the compulsory rate is 12%. You can also make voluntary contributions. Several examples on this page were written at the 2024–25 rate of 11.5% and still use it, so work with whatever rate the question states rather than the one you remember.
Net return
Use $r_{\text{net}}$ not $r_{\text{return}}$ in all calculations. A 7% return with 1.2% fees = 5.8% net, that is the rate you actually receive.
Compounding effect of fees
Every dollar lost in fees cannot compound. The true cost of fees is not 1% of your balance, it is 1% compounded over every remaining year.
03
What you'll master
Know

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)
Understand

Concepts

  • Why fees compound to massive differences over decades
  • The trade-off between investment return and risk
  • How salary growth changes the model
Can do

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
04
Key terms
SuperannuationA compulsory Australian retirement savings system. Employers contribute a percentage of salary to a super fund.
Gross returnThe investment return before fees are deducted: $r_{\text{return}}$.
Net return$r_{\text{net}} = r_{\text{return}} - r_{\text{fees}}$, the effective growth rate after fees.
Management feeAnnual fee charged as a percentage of the account balance, typically 0.5%–2%.
Contribution ratePercentage of salary contributed to super. The compulsory employer rate is 12% from 1 July 2025; it was 11.5% in 2024–25.
Super projectionEstimated balance at retirement, calculated using the closed-form annuity formula with net return.

Build the full model

Assemble contributions, growth and time into one working superannuation model.

05
The full superannuation model
core concept

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.

Superannuation calculation as a 3-step sequence with result footnote

The compound growth component ($\$814$k) dwarfs the total contributions ($\$322$k) by nearly 3:1.

$$A_n = A_0(1+r_{\text{net}})^n + C \times \dfrac{(1+r_{\text{net}})^n - 1}{r_{\text{net}}}$$
The silent killer of retirement wealth. A 1% fee sounds trivial. Over 40 years on a growing balance, it can cost more than $600,000, exceeding the total contributions of many workers. Every dollar lost in fees is a dollar that cannot compound. The effect is exponential, not linear.

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%.

Work the examples

Follow three worked superannuation problems end to end.

Worked examples · 3 in a row, reveal as you go

PROBLEM 1 · FULL SUPER PROJECTION

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.

1
$C = 75{,}000 \times 0.115 = \$8{,}625 \text{ per year}$
$r_{\text{net}} = 0.068 - 0.011 = 0.057$ (5.7%)
$n = 65 - 30 = 35 \text{ years}$
Identify contribution, net return, and time horizon.
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PROBLEM 2 · FEE COMPARISON

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?

1
New $r_{\text{net}} = 0.068 - 0.003 = 0.065$ (6.5%)
$A_{35} = 25{,}000(1.065)^{35} + 8{,}625 \times \dfrac{(1.065)^{35} - 1}{0.065}$
$= 25{,}000(8.946) + 8{,}625(122.25) = 223{,}650 + 1{,}054{,}406 = \mathbf{\$1{,}278{,}056}$
Recalculate with the lower fee rate.
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PROBLEM 3 · RECURRENCE TABLE (FIRST 3 YEARS)

$A_0 = \$20{,}000$, $r_{\text{net}} = 0.058$, $C = \$9{,}200$ p.a. Show the first 3 years using recurrence.

1
$A_{n+1} = 1.058 A_n + 9{,}200$, $\quad A_0 = 20{,}000$
Write the recurrence relation with the net return.
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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?

See what fees do

Read the fee impact table and say what a small fee costs over a working life.

The hidden cost of fees · why 1% matters so much

09
The fee impact table
real numbers

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?

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Drill it and revisit

Run the drill, then return to your opening answer and name what has changed.

Quick-fire practice · 5 super calculations

1

Salary $\$60{,}000$, contribution rate 11.5%. What is $C$?

2

Gross return 7.5%, fees 1.2%. What is $r_{\text{net}}$?

3

Write the recurrence relation: $A_0 = \$15{,}000$, $r_{\text{net}} = 5.8\%$, $C = \$8{,}625$ p.a.

4

From the fee table, how much does switching from 1.5% to 0.5% fees save over 35 years?

5

$A_0 = \$15{,}000$, $r_{\text{net}} = 0.062$, $C = \$6{,}900$ 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.

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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
10
Revisit your thinking

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.

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Practise superannuation

Write full short-answer responses, then check them against the model answers.

01
Multiple choice
+5 XP per correct · +25 XP all-correct

Pick your answer, then rate your confidence. That tells the system what to drill next. Each retry pulls a fresh mix from the bank.

02
Short answer
ApplyBand 43 marks

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)

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ApplyBand 43 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)

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AnalyseBand 54 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) Verify $A_2$ using the closed form, and explain why the two methods must agree. (4 marks)

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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) $A_1 = 1.058(20{,}000)+9{,}200 = \$30{,}360$; $A_2 = 1.058(30{,}360)+9{,}200 = \$41{,}320.88$ [2]. (c) Closed form: $A_2 = 20{,}000(1.058)^2 + 9{,}200 \times [(1.058)^2-1]/0.058 = 22{,}387.28 + 18{,}933.60 = \$41{,}320.88$, the same value to the cent [1]. The two methods must agree because the closed form is what you get by unrolling the recurrence, so any gap you see is arithmetic you rounded on the way, not a real difference between the methods.