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hscscience Maths Adv · Y12
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Module 7 · L16 of 20 ~40 min ⚡ +100 XP available

Comparing Investment Products

Not all investments are created equal. A term deposit guarantees 4.5% but locks your money away. A growth portfolio targets 9% but can lose 20% in a bad year. In this lesson, you will compare products mathematically, calculating net returns, adjusting for fees and tax, and understanding why the highest rate is not always the best choice.

Today's hook, A managed fund advertises 8% returns. After 1.5% fees and 32.5% tax, the real return is 4.37%. Meanwhile, a "boring" term deposit at 5% beats it, guaranteed. The maths of comparison is more powerful than the marketing.
0/5QUESTS

Get oriented

Recall what you already know, meet the key ideas and settle the terms.

Beyond the syllabus. This whole lesson is extension: fees, tax, risk and product recommendation are valuable financial literacy but exceed the two core content groups of this focus. For the exam, master reducing-balance loans and annuities — and read this comparison of investment products as life preparation.
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

Product A: 5% p.a., guaranteed, no fees.

Product B: 8% p.a. average return, 1.5% fees, returns vary year to year.

Over 20 years which product would you expect to grow faster? Is there any scenario where Product A wins?

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02
The four-step comparison method
+5 XP to read

The mathematically correct way to compare investments is to calculate the net return after all fees and taxes, then project it over your time horizon.

Every comparison follows the same four steps. Skip any step and your comparison is meaningless, you are comparing the wrong numbers.

  1. Step 1: Find the gross return (advertised rate).
  2. Step 2: Subtract fees: $r_{\text{net}} = r_{\text{gross}} - r_{\text{fees}}$
  3. Step 3: Apply tax if applicable: $r_{\text{after-tax}} = r_{\text{net}} \times (1 - t)$
  4. Step 4: Compare using $FV = PV(1 + r_{\text{net}})^n$ for each product.
Four-step investment comparison process migrated to a sequence layout.
$r_{\text{net}} = r_{\text{gross}} - r_{\text{fees}}$
03
What you'll master
Know

Key facts

  • How to compare investment products using net return
  • The impact of fees on long-term growth
  • Tax treatment of different investments
Understand

Concepts

  • The risk-return trade-off and time horizon interaction
  • Why compounding magnifies small return differences
  • When guaranteed returns beat variable returns
Can do

Skills

  • Calculate net and after-tax returns
  • Compare products using $FV = PV(1+r)^n$
  • Evaluate fee impact in dollar terms over long periods
  • Recommend products for different risk profiles and time horizons
04
Key terms
Gross returnThe advertised return before fees and taxes are deducted.
Net return$r_{\text{net}} = r_{\text{gross}} - r_{\text{fees}}$, the return after management fees.
After-tax return$r_{\text{after-tax}} = r_{\text{gross}} \times (1 - t)$, what you actually keep after income tax.
Future value (FV)$FV = PV(1+r)^n$, the projected final value of the investment.
Risk-return trade-offHigher expected returns always come with higher risk (volatility or potential loss).
Capital preservationPrioritising the safety of the original investment over growth, important for short time horizons.

Compare the products on the numbers

Weigh fees, frequency and access alongside the headline rate.

05
Comparing investment products, the numbers
core concept

The advertised rate is almost never the true return. To compare honestly, you must calculate the net return and project the future value.

$$FV = PV(1 + r_{\text{net}})^n$$

$PV$ = initial investment, $r_{\text{net}}$ = annual net return (after fees), $n$ = years

Example, $50,000 over 20 years:

ProductGrossFeesNetFV (20 yrs)
Term Deposit4.5%0%4.5%$120,300
Managed Fund7.0%1.0%6.0%$160,400
Growth Portfolio9.0%1.5%7.5%$212,200

The growth portfolio yields 76% more than the term deposit after 20 years, but only if it achieves its average return. In a market crash, the term deposit holder sleeps soundly while the growth investor can lose 20% of capital.

The 1% fee problem. A 1% annual management fee on a $\$50,000$ investment over 20 years does not cost $\$500$, it costs $27,735 in lost compounding. Small percentages compound into enormous dollar differences. Always ask: what is the fee in dollar terms over my full time horizon?

Step-by-step comparison: Gross rate → subtract fees → apply tax → calculate $FV = PV(1+r)^n$ → compare; After-tax return: $r_{\text{after-tax}} = r_{\text{gross}} \times (1 - t)$. Always convert before comparing.

Pause, copy the after-tax return formula $r_{\text{after-tax}} = r_{\text{gross}} \times (1-t)$ and the comparison chain (gross → subtract fees → apply tax → compute $FV = PV(1+r)^n$) into your book.

Quick check: A managed fund advertises 7% p.a. with 1.2% annual fees. What is the correct net return to use when comparing future values?

Work the examples

Follow three worked product comparisons end to end.

Worked examples · 3 comparison scenarios

PROBLEM 1 · TERM DEPOSIT vs BALANCED FUND

$30,000 invested for 15 years. Product A: term deposit at 4.8% p.a., no fees. Product B: balanced fund at 6.5% p.a. gross, 0.8% fees. Which product has the higher FV? By how much?

1
Product A: $FV = 30{,}000(1.048)^{15}$
Apply the FV formula directly, no fees to subtract.
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PROBLEM 2 · AFTER-TAX COMPARISON

$20,000 over 10 years. Product X: high-interest savings at 6% p.a., taxed at 32.5%. Product Y: index fund at 7% p.a. net, returns taxed as capital gains (15%). Which wins after tax?

1
Product X after-tax: $6\% \times (1 - 0.325) = 6\% \times 0.675 = 4.05\%$
Apply the after-tax formula: $r \times (1-t)$.
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PROBLEM 3 · FEE SENSITIVITY

A managed fund has gross return 7% p.a. At what fee level does it underperform a term deposit at 4.5% over 20 years (assuming $50,000 initial, same tax treatment)?

1
For the managed fund to match the term deposit: $r_{\text{net}} \geq 4.5\%$
Both must produce at least the same FV for the managed fund to be worth it.
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Did you get this? True or false: the product with the highest advertised gross return is always the best investment.

06
The risk-return trade-off
core concept

We just saw that a 1% fee on $\$50,000$ over 20 years costs $\$27,735$ in lost compounding, numbers make the choice clear. That raises a question: numbers alone don't tell you which product suits your situation, what role does risk tolerance and time horizon play? This card answers it → matching short/medium/long-term horizons to appropriate risk levels using the risk-return trade-off.

Higher expected returns always come with higher risk. The key question is not "what is the highest return?" but "can you afford the downside?"

Short-term (1–3 years)
Prioritise capital preservation. Term deposits or high-interest savings accounts. Cannot risk a 20% market drop when you need the money in 2 years.
Medium-term (5–10 years)
Balanced approach. Managed funds or balanced portfolios. Some exposure to growth assets with a safety buffer in defensive assets.
Long-term (15+ years)
Growth assets. Time absorbs volatility. A 25-year-old investing for retirement has 40 years for compound growth to dominate short-term fluctuations.

Mathematical insight: Over long time horizons, the standard deviation of annual returns matters less because good years offset bad years. This is why young investors can afford growth assets, time is their risk reducer.

Over 40 years a 7.5% growth portfolio pulls far ahead of a 4.5% term deposit through compounding.

At 40 years, 7.5% net grows roughly 3× more than 4.5%. Time horizon is the deciding factor.

Risk-return trade-off: higher returns → higher risk (capital loss or volatility); Time horizon changes the appropriate product: short-term = safe; long-term = growth

Pause, copy the risk-return principle (higher return = higher volatility/capital risk) and the horizon rule (short-term: capital preservation; medium: balanced; long-term: growth assets) into your book.

Fill in the blank: To find the after-tax return: $r_{\text{after-tax}} = r_{\text{gross}} \times (1 - \_\_\_)$. For a savings account at 6% taxed at 32.5%, the after-tax return is ___% .

Avoid the traps

Stop comparing headline rates without adjusting for fees and frequency.

Common errors · the 3 traps that cost marks

Trap 01
Comparing gross returns without subtracting fees
A fund at 9% gross and 1.5% fees has a net return of 7.5%. Comparing 9% vs a term deposit's 4.5% is meaningless, you must compare net. Always subtract fees before calculating FV.
Trap 02
Ignoring tax treatment differences
A savings account at 6% taxed at 32.5% returns 4.05% after tax. An index fund at 6% with capital gains tax at 15% returns 5.1% after tax. The same gross rate produces wildly different outcomes depending on how it's taxed.
Trap 03
Recommending the same product for all time horizons
A growth portfolio is the best choice for 40 years, but a terrible choice for 3 years. The maths changes because the risk of a 20% loss in Year 1 is devastating for a 3-year investor but recoverable for a 40-year investor.

Match each investor to the most appropriate product:

  • 25-year-old saving for retirement (40 years)
  • 60-year-old needing money in 3 years
  • 45-year-old saving for 15 years
  • Term deposit
  • Balanced fund
  • Growth portfolio

Drill it and revisit

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

Quick-fire practice · 4 calculations

1

$50,000 over 20 years. Term deposit at 4.5%, managed fund net 6%, growth portfolio net 7.5%. Calculate FV for each product.

2

A managed fund increases fees from 1% to 2%. Gross return stays at 7%. What is the new net return? Over 20 years on $50,000, how much does the 1% fee increase cost in dollar terms?

3

A savings account pays 6% p.a. taxed at 32.5%. Is this better or worse than a term deposit at 4.5% p.a. (not taxed separately)? Show the after-tax calculation.

4

A 25-year-old invests $50,000. Recommend a product for a 40-year retirement horizon. Use numbers to justify: what FV does the growth portfolio (7.5% net) achieve vs term deposit (4.5%)?

Did you get this? True or false: a 60-year-old investor who needs their money in 5 years should generally invest in a growth portfolio rather than a term deposit.

09
Revisit your thinking

Earlier: Product A (5% guaranteed) vs Product B (8% gross, 1.5% fees). Product B's net return is 6.5%. Over 20 years: $50,000(1.065)^{20} = \$176,000$ vs Product A's $50,000(1.05)^{20} = \$132,665$. Product B wins by $\$43,335$.

However, Product A wins if: (1) the investor needs the money within 1–3 years and cannot risk a market downturn; (2) Product B underperforms significantly; (3) the investor values certainty over maximum return. Risk tolerance and time horizon matter as much as the numbers.

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Practise product comparison

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.

02
Short answer
ApplyBand 43 marks

Q1. An investor has $30,000. Product A: term deposit at 4.5% p.a., no fees. Product B: balanced fund at 6.5% p.a. gross, 0.8% fees. (a) State the net return for each product. (b) Calculate the FV of each product after 15 years. (c) State which product wins and by how much. (3 marks)

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ApplyBand 43 marks

Q2. A managed fund earns 6% p.a. gross, taxed at 32.5%. (a) Find the after-tax return. (b) Compare to a term deposit at 4.5%. (c) Which product gives a higher after-tax return? (3 marks)

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AnalyseBand 54 marks

Q3. $100,000 is invested in a growth portfolio at 8% p.a. net for 25 years, and simultaneously in a term deposit at 4.5% p.a. for the same period. (a) Calculate both FVs. (b) Find the dollar difference. (c) Explain why the same mathematical result does not mean the growth portfolio is always the better recommendation for all investors. (4 marks)

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Comprehensive answers (click to reveal)

Drill answers:

1. TD: $50,000(1.045)^{20} = \$120,300$. MF: $50,000(1.06)^{20} = \$160,400$. GP: $50,000(1.075)^{20} = \$212,200$.

2. New net = 5%. $FV = 50,000(1.05)^{20} = \$132,665$. Previously $\$160,400$. The 1% fee increase costs $\$27,735$ over 20 years.

3. After-tax savings = $6\% \times 0.675 = 4.05\%$. Term deposit at 4.5% > 4.05%, so term deposit wins.

4. Growth at 7.5% for 40 years: $50,000(1.075)^{40} = \$50,000 \times 17.4 = \$871,000$. TD at 4.5%: $50,000(1.045)^{40} = \$50,000 \times 5.82 = \$291,000$. Recommend growth portfolio, 40-year horizon allows time to absorb downturns.

Q1 (3 marks): (a) Product A: 4.5%. Product B: 6.5% − 0.8% = 5.7% [1]. (b) $FV_A = 30,000(1.045)^{15} = \$58,300$ [1]; $FV_B = 30,000(1.057)^{15} = \$69,240$ [1]. (c) Product B wins by $\$10,940$.

Q2 (3 marks): (a) After-tax = $6\% \times (1 - 0.325) = 4.05\%$ [2]. (b) Term deposit: 4.5% after-tax (assumed no tax impact). 4.05% < 4.5% [1]. (c) Term deposit wins.

Q3 (4 marks): (a) Growth: $100,000(1.08)^{25} = \$684,850$ [1]; TD: $100,000(1.045)^{25} = \$296,000$ [1]. (b) Difference $= \$388,850$ [1]. (c) Growth portfolio involves market volatility, a 60-year-old needing money in 5 years cannot risk a significant loss. Time horizon and risk tolerance determine suitability, not just expected returns [1].