Superannuation models | Year 12

01 / LEARN

The idea, step by step

Separate contribution flows from investment growth

A superannuation model is a savings model with contributions and possible deductions. Use only the contribution and tax rules supplied in the question. If a contribution C has a stated tax fraction t, the net amount entering the account is C(1−t). Do not treat a salary contribution percentage as an investment return.

State whether contributions and fixed fees occur before or after the period return. Here $B_{k}$ is the closing balance at year k, $C_{k}$ is that year’s gross contribution and $F_{k}$ is that year’s fee. Contributions and fees occur at the year end. With constant amounts, the net contribution is an ordinary annuity cash flow.

B_{k} = B_{k - 1} (1 + i) + C_{k} (1 - t) - F_{k}

Changing contributions and uncertain returns

A salary may grow, changing contributions from year to year. Build a row for each year and apply the recurrence using that year’s contribution. A fixed dollar fee has a different effect from a percentage charge; do not subtract a dollar amount from a percentage.

A constant investment rate is a simplifying scenario. Realised returns can vary and their order matters when contributions or withdrawals occur. Compare models with the same starting balance, timing and assumptions, and report the limits of the comparison.

A common trap

Adding the gross contribution and then forgetting a stated contribution deduction.

Instead: Calculate the net contribution first and use that amount in the balance model.

02 / WORKED EXAMPLES

See the thinking

Example 1

Build the model

For this model, salary is AUD 50,000, the annual contribution is 10% of salary, and 15% is deducted from contributions. Find the net annual contribution.

Gross contribution is $50000 \times 0.10 = 5000$ .
Net contribution is $5000 \times 0.85 = 4250$ .

AUD 4,250.00

Example 2

Use the model to make a decision

Start with AUD 20,000. A net AUD 3,000 is added at each year end for 5 years. Returns are 4% annually and a fixed AUD 100 year-end fee is charged. Find the final balance.

The net year-end cash flow is $3000 - 100 = 2900$ .
Balance is $20000 {(1.04)}^{5} + 2900 ({(1.04)}^{5} - 1) / 0.04$ .

AUD 40,040.39

Check your understanding

A fund starts at AUD 8,000, earns 5%, then receives a net AUD 2,200 contribution and pays a fixed AUD 90 fee at year end. Find its new balance.

Show answer

AUD 10,510.00

Interest is $8000 \times 0.05 = 400$ . Balance is $8000 + 400 + 2200 - 90 = 10510$ .

03 / WORKSHEET

Your turn

6 questions · 17 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

A model has an annual gross contribution of AUD 6,400 and a stated contribution deduction of 12%. Find the net contribution.
3 marks
A fund starts at AUD 8,000, earns 5%, then receives a net AUD 2,200 contribution and pays a fixed AUD 90 fee at year end. Find its new balance.
3 marks
A constant net contribution is AUD 2,500 at each year end. At 4%, starting from zero, find the balance after 12 years.
3 marks
A balance of AUD 10,000 earns 5% in year 1 and −3% in year 2. Add AUD 2,000 at each year end. Find the final balance.
3 marks
Compare fixed year-end fees of AUD 80 and AUD 150 over 10 years at 4%, with all other cash flows identical. Find the difference in final balances.
3 marks
Explain why a projected balance based on 6% every year is not a guaranteed result.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A model has an annual gross contribution of AUD 6,400 and a stated contribution deduction of 12%. Find the net contribution.
3 marks
Net is 6400(1−0.12).
$6400 \times 0.88 = 5632$ .
AUD 5,632.00
A fund starts at AUD 8,000, earns 5%, then receives a net AUD 2,200 contribution and pays a fixed AUD 90 fee at year end. Find its new balance.
3 marks
Interest is $8000 \times 0.05 = 400$ .
Balance is $8000 + 400 + 2200 - 90 = 10510$ .
AUD 10,510.00
A constant net contribution is AUD 2,500 at each year end. At 4%, starting from zero, find the balance after 12 years.
3 marks
This is an ordinary annuity with $R = 2500, i = 0.04$ and $n = 12$ .
Use $R ({(1 + i)}^{n} - 1) / i$ .
AUD 37,564.51
A balance of AUD 10,000 earns 5% in year 1 and −3% in year 2. Add AUD 2,000 at each year end. Find the final balance.
3 marks
After year 1: $10000 \times 1.05 + 2000 = 12500$ .
After year 2: $12500 \times 0.97 + 2000 = 14125$ .
AUD 14,125.00
Compare fixed year-end fees of AUD 80 and AUD 150 over 10 years at 4%, with all other cash flows identical. Find the difference in final balances.
3 marks
The fee difference is AUD 70 each year.
Its accumulated effect is the future value of ten end-of-year AUD 70 payments.
AUD 840.43
Explain why a projected balance based on 6% every year is not a guaranteed result.
2 marks
Identify the assumed quantities.
A valid calculation only describes what follows if those assumptions hold.
The return is an assumed constant; actual yearly returns, contributions, fees and timing may differ.

Checking saved progress…

Continue learning

Annuities providing an income

Next lesson

Curriculum reference & lesson scope

SACE Board of South Australia

Stage 2 General Mathematics financial models: investments and annuities, superannuation, income streams and borrowing. Original practice uses supplied hypothetical rates, taxes and fees; statutory or commercial conditions are not inferred.

Official curriculum source ↗

Back to Financial mathematics