Mathematics Advanced • Year 12 • Module 7 • Lesson 16
Comparing Investment Products
Practise HSC-style writing on net returns, after-tax returns and fee-sensitive product comparison.
1. Short-answer questions
1.1 $30,000 is invested for 15 years. Product A pays 4.5% p.a. (no fees). Product B pays 7.0% p.a. gross with 1.5% management fees. (a) Find the net return for Product B. (b) Find the FV of each product to the nearest dollar. 3 marks Band 3
1.2 A managed fund returns 6.0% p.a. before tax. The investor's marginal tax rate is 32.5%. (a) Calculate the after-tax return. (b) State whether this product beats a term deposit paying 4.5% p.a. (no tax-deferred wrapper) and justify with one line. 3 marks Band 3-4
1.3 $100,000 is invested for 25 years. Product P: 8.0% p.a. (net). Product Q: 6.5% p.a. (net). (a) Find the FV of each, to the nearest dollar. (b) Find the dollar difference. (c) State, in one sentence, the practical condition under which an investor should still choose Product Q despite its lower return. 4 marks Band 4
Stuck on 1.3(c)? Refer back to the risk-tolerance / drawdown discussion in the lesson — Q may have lower volatility.2. Extended response
2.1 An investor has $50,000 to invest for 20 years. Three products are available, all advertised at headline rates ≤ 8%.
Term Deposit: 4.5% p.a., guaranteed, no fees, no internal tax.
Managed Fund: 7.0% p.a. gross, 1.0% fees, taxed at the investor's marginal rate of 32.5%.
Growth Portfolio: 9.0% p.a. gross average return, 1.5% fees, held in a super wrapper taxed at 15%.
(a) For each product, compute (i) net return after fees and (ii) the rate that actually compounds for the investor after tax. Show working.
(b) Find the 20-year FV of each product to the nearest dollar. Rank them.
(c) Explain in 2–3 sentences why the headline rate alone is insufficient to compare these products, referencing both the fee subtraction and the tax-vehicle effect. 8 marks Band 5-6
Explicit marking criteria
Part (a) — 3 marks
• 1 mark — correct rnet for all three products (TD 4.5%; MF 6.0%; GP 7.5%).
• 2 marks — correct after-tax rate for all three (TD 4.5%; MF 4.05%; GP 6.375%) with (1 − t) applied to the post-fee figure.
Part (b) — 3 marks
• 2 marks — all three FVs to the nearest dollar.
• 1 mark — correct ranking GP > MF > TD with figures consistent with (a).
Part (c) — 2 marks
• 1 mark — names the fee subtraction as the first reason a headline rate misleads.
• 1 mark — names the tax-vehicle effect (15% super tax vs 32.5% marginal) as the second reason, with a numeric illustration.
Your response:
Stuck on (c)? Quote at least one specific number — e.g. "MF's after-tax rate of 4.05% is actually lower than TD's 4.5%".How did this worksheet feel?
What I'll revisit before next class:
1.1 — Net return and FV (3 marks)
Sample response. (a) rnet,B = 7.0 − 1.5 = 5.5%. (b) Product A: FV = 30,000 × (1.045)¹⁵ = 30,000 × 1.93528 = $58,059. Product B: FV = 30,000 × (1.055)¹⁵ = 30,000 × 2.23248 = $66,974. Product B wins by $8,915.
Marking notes. 1 mark — correct net return for B. 1 mark — correct FVA. 1 mark — correct FVB. A common error is using r = 7% (gross) for B; that gives FV ≈ $82,800 and scores 0/1 for the FVB mark.
1.2 — After-tax comparison (3 marks)
Sample response. (a) rafter-tax = 6.0 × (1 − 0.325) = 6.0 × 0.675 = 4.05%. (b) The managed fund's after-tax return (4.05%) is lower than the term deposit's 4.5%, so the term deposit wins after tax. A taxable managed fund needs a gross return above about 6.7% just to match a 4.5% term deposit at this marginal rate.
Marking notes. 1 mark — correct application of (1 − t). 1 mark — correct numerical value 4.05%. 1 mark — explicit comparison stating term deposit wins after tax.
1.3 — P vs Q on $100,000 over 25 years (4 marks)
Sample response. (a) P: FV = 100,000 × (1.08)²⁵ = 100,000 × 6.8485 = $684,848. Q: FV = 100,000 × (1.065)²⁵ = 100,000 × 4.8277 = $482,770. (b) Difference = $202,078. (c) Q is still correct when the investor cannot tolerate the higher volatility of P — for example, if Q's worst-year drawdown is 5% but P's is 30%, an investor near drawdown needs Q to preserve capital.
Marking notes. 1 mark — correct FVP. 1 mark — correct FVQ. 1 mark — correct dollar difference. 1 mark — justified risk-based reason for choosing Q. Bald "Q is safer" without a numeric or risk reference scores 0/1 on (c).
2.1 — Three products at < 8% headline (8 marks): sample Band-6 response with annotations
Sample Band-6 response.
(a) Net and after-tax rates.
Term Deposit. rnet = 4.5%. No internal or marginal tax stated in TD wrapper → rafter-tax = 4.5%. [net-mark]
Managed Fund. rnet = 7.0 − 1.0 = 6.0%. rafter-tax = 6.0 × (1 − 0.325) = 4.050%. [net + after-tax marks]
Growth Portfolio. rnet = 9.0 − 1.5 = 7.5%. rafter-tax = 7.5 × (1 − 0.15) = 6.375%. [net + after-tax marks]
(b) 20-year FVs and ranking.
TD: FV = 50,000 × (1.045)²⁰ = 50,000 × 2.41171 = $120,586. [1 mark]
MF: FV = 50,000 × (1.0405)²⁰ = 50,000 × 2.21893 = $110,946. [1 mark]
GP: FV = 50,000 × (1.06375)²⁰ = 50,000 × 3.43498 = $171,749. [1 mark]
Ranking: GP > TD > MF. Note that the apparently "safe" managed fund finishes worse than the term deposit once tax and fees are deducted.
(c) Why the headline rate cannot be used alone. Two distinct effects mean equal headline rates do not produce equal investor returns. (1) Fees. The managed fund's 7.0% gross becomes 6.0% net once 1.0% in fees is removed; only the net portion is left to compound through (1 + r)ⁿ. (2) Tax wrapper. The growth portfolio sits inside a super wrapper taxed at 15%, while the managed fund is taxed at the investor's 32.5% marginal rate — so a 1.5 pp gross-return advantage for the growth portfolio becomes a 2.325 pp after-tax advantage (6.375% vs 4.050%), magnifying it through 20 years of compounding to a $60,800 final-balance gap. [2 marks]
Total: 8/8.
Band descriptors for marker.
Band 3: Two of three net returns correct, no tax adjustment or tax applied to gross not net. FVs computed but ranking inconsistent with figures. ≈ 3-4 marks.
Band 4: All net returns correct, after-tax for at least two products correct, all FVs computed but explanation in (c) restates rather than connects to fee + tax-wrapper effect. ≈ 5-6 marks.
Band 5: All calculations correct including the (1 − t) on the post-fee return. Ranking justified by formula structure, but (c) only mentions one of fee or tax. ≈ 6-7 marks.
Band 6: Full calculations to the dollar; ranking correct (and surprising — MF < TD); (c) explicitly references both fee subtraction and the tax-wrapper effect with a numeric illustration. 8/8.