Mathematics Advanced • Year 12 • Module 7 • Lesson 16
Comparing Investment Products
Apply net-return, after-tax and time-horizon thinking to realistic investment-product decisions.
Problem 1 — Two products from a friend (the "Think First" scenario)
A friend offers two products on $50,000 for 20 years:
Product A: 5% p.a., guaranteed, no fees.
Product B: 8% p.a. average return, 1.5% fees, returns vary year to year.
Set up: What are we solving for?
(i) Find the FV of Product A and Product B (using its average net return) over 20 years. 2 marks
(ii) State which product wins on average and by how many dollars. 1 mark
(iii) Identify two scenarios in which Product A is still the rational choice. 3 marks
Stuck? Revisit lesson § Think First and § Risk-Return Trade-off.Problem 2 — Managed fund fee creep
An investor places $50,000 in a managed fund advertised at 7% p.a. gross with 1% fees and a 20-year horizon. Two years in, the fund's product disclosure changes and fees rise to 2%.
Set up: What are we solving for?
(i) State the new net return and the new 20-year FV (assume the fee change applied from year 0 for simplicity). 2 marks
(ii) Calculate the dollar cost of the 1% fee increase over 20 years. 1 mark
(iii) Determine the fee level at which the managed fund just matches the 4.5% term deposit FV. Use this to write a one-line decision rule the investor could apply when reviewing the product. 3 marks
Problem 3 — Choosing a tax-efficient vehicle
A 40-year-old has $25,000 to invest for 25 years. Three options:
Option 1: high-interest savings, 4.5% p.a. interest taxed at the investor's marginal rate of 37%.
Option 2: balanced super contribution, 6.5% p.a. gross with 0.8% fees, earnings taxed at the 15% super rate.
Option 3: growth portfolio in an investment bond, 7.5% p.a. gross with 1.5% fees, internal tax 30%.
Set up: What are we solving for?
(i) For each option, find the after-fee return then apply (1 − t) to obtain the rate that actually compounds for the investor. 3 marks
(ii) Find the FV of $25,000 after 25 years in each option. Rank them. 3 marks
(iii) Explain in one sentence why Option 2 can beat Option 3 even though its headline rate is lower. 1 mark
Stuck? Apply the lesson's rafter-tax = rgross × (1 − t) but first net out fees.Problem 4 — Same product, different lives
The lesson's growth portfolio earns 7.5% net. Term deposit earns 4.5% net. Two investors compare them on $50,000.
Investor A: 25 years old, saving for retirement in 40 years.
Investor B: 60 years old, needs the money in 5 years for a house move.
Set up: What are we solving for?
(i) Compute the FV of each product for each investor. 3 marks
(ii) State the absolute dollar gap (growth − term deposit) for each investor and the percentage gap relative to the term deposit. 2 marks
(iii) Recommend a product for each investor and justify in one sentence each, referencing both the FV gap and the lesson's risk-time-horizon principle. 2 marks
Problem 5 — Reading the marketing carefully
A bank ad reads "Earn 6.5% p.a. on our top-rated managed fund." The PDS reveals: management fee 1.2%, performance fee 0.3%, investor marginal tax 32.5%, and projected inflation 2.5% p.a.
Set up: What are we solving for?
(i) Compute the net return after fees, then the after-tax return for the investor. 2 marks
(ii) Subtract inflation to estimate the real return. Find the FV in nominal dollars and in today's-dollars on a $20,000 deposit over 15 years. 3 marks
(iii) Write a one-line warning a financial-literacy teacher could quote in class about the gap between the advertised 6.5% and what the investor actually keeps. 2 marks
Stuck? Revisit lesson § Misconceptions — gross vs net vs after-tax vs real returns.How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Two products on $50,000 over 20 years
Set up. We are computing the FV of each product (using B's average net return) and identifying when the guaranteed lower-rate product is still the right call.
(i) Product A: FV = 50,000 × (1.05)²⁰ = 50,000 × 2.6533 = $132,665. Product B (rnet = 8 − 1.5 = 6.5%): FV = 50,000 × (1.065)²⁰ = 50,000 × 3.5236 = $176,182.
(ii) Product B wins by 176,182 − 132,665 = $43,517 (≈ 33% more).
(iii) Product A still wins when: (1) the investor needs the money within 1–3 years and cannot risk a downturn at the wrong moment; (2) Product B underperforms its average for the first decade and the investor would be forced to withdraw before recovery; (3) the investor places higher value on certainty than on the expected $43,500 upside (risk aversion / sleep test).
Problem 2 — Fee creep on the managed fund
Set up. We are quantifying the dollar damage of a fee increase and finding the break-even fee at which the fund just matches a guaranteed term deposit.
(i) New rnet = 7 − 2 = 5%. FV = 50,000 × (1.05)²⁰ = $132,665.
(ii) Original FV (1% fee, 6% net) = 50,000 × (1.06)²⁰ = $160,356. Cost of fee increase = 160,356 − 132,665 = $27,691 over 20 years.
(iii) Break-even: rnet must equal 4.5%, so fee = 7 − 4.5 = 2.5%. Decision rule: "If the managed fund's combined fees exceed 2.5% of assets per year, switch to the term deposit — the guaranteed 4.5% will beat the post-fee return at any 20-year horizon."
Problem 3 — Tax-efficient vehicle
Set up. We are computing the rate that actually compounds for the investor in each vehicle (net of fees and tax), then projecting $25,000 over 25 years.
(i) Option 1: rnet = 4.5%; rafter-tax = 4.5 × (1 − 0.37) = 2.835%. Option 2: rnet = 6.5 − 0.8 = 5.7%; rafter-tax = 5.7 × (1 − 0.15) = 4.845%. Option 3: rnet = 7.5 − 1.5 = 6.0%; rafter-tax = 6.0 × (1 − 0.30) = 4.200%.
(ii) Option 1: FV = 25,000 × (1.02835)²⁵ = 25,000 × 2.0102 = $50,255. Option 2: FV = 25,000 × (1.04845)²⁵ = 25,000 × 3.250 = $81,259. Option 3: FV = 25,000 × (1.042)²⁵ = 25,000 × 2.7860 = $69,649. Ranking: Option 2 > Option 3 > Option 1.
(iii) Option 2 beats Option 3 because the super tax rate of 15% is so much lower than the investment-bond's 30% internal tax that it more than offsets Option 3's 1.0 pp headline-rate advantage.
Problem 4 — Same product, different lives
Set up. We are comparing the term-deposit and growth-portfolio FVs at two very different time horizons.
(i) Investor A (40 yr): Term deposit FV = 50,000 × (1.045)⁴⁰ = 50,000 × 5.8164 = $290,818; Growth FV = 50,000 × (1.075)⁴⁰ = 50,000 × 18.044 = $902,180. Investor B (5 yr): Term deposit FV = 50,000 × (1.045)⁵ = $62,310; Growth FV = 50,000 × (1.075)⁵ = $71,782.
(ii) Investor A gap = $611,362, or 210% of the term deposit. Investor B gap = $9,472, or 15% of the term deposit.
(iii) Investor A — growth portfolio: a $611k expected upside over 40 years justifies the volatility, which has time to average out. Investor B — term deposit: a $9.5k expected upside is not worth a 20% market-crash risk on capital needed in 5 years (the lesson's short-horizon rule).
Problem 5 — Real vs nominal on the advertised 6.5%
Set up. We are converting a headline gross rate into the after-fee, after-tax and after-inflation return the investor actually keeps, then projecting both nominal and real FVs.
(i) Total fees = 1.2 + 0.3 = 1.5%. rnet = 6.5 − 1.5 = 5.0%. rafter-tax = 5.0 × (1 − 0.325) = 3.375%.
(ii) Real return ≈ 3.375 − 2.5 = 0.875%. Nominal FV = 20,000 × (1.03375)¹⁵ = 20,000 × 1.6432 = $32,864. Today's-dollars FV = 20,000 × (1.00875)¹⁵ = 20,000 × 1.1394 = $22,788.
(iii) Sample warning: "The advertised 6.5% becomes about 0.9% in real terms once fees, marginal tax and inflation are stripped out — turning a 'high-return fund' into a barely-keeps-pace product for an investor on the 32.5% bracket."