Mathematics Standard • Year 12 • Investment and Loans • Lesson 15
Brokerage and Investment Choice, Reasoning
Find where a brokerage rule switches over, then evaluate a claim about four investments that is true on one measure and wrong on three.
1. The switch-over point
A different broker charges the greater of $19.95 or 0.12% of the trade value. 2 marks each
Q1.1 Find the trade value at which the two rules cost exactly the same.
Q1.2 State which rule applies on a trade of $10,000 and which on a trade of $25,000, without calculating either fee.
2. Comparing four investments
Priya has $30,000 and will not need it for 4 years. A savings account pays 3.9% p.a. compounded annually; a 4-year term deposit pays 4.5% p.a. compounded annually. 8 marks total
Q2.1 Find the value of each after 4 years, correct to the nearest cent.
Q2.2 Find the difference.
Q2.3 Priya says: "the term deposit beats the savings account, so it is the best of the four options." Evaluate that on return, risk, liquidity and cost to enter.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1
Set 0.0012 × V = 19.95, so V = 19.95 ÷ 0.0012 = $16,625 [2]. Check: 0.12% of $16,625 = $19.95.
Q1.2
$10,000 is below the break-even, so the flat $19.95 applies [1]. $25,000 is above it, so the percentage applies [1]. Knowing the break-even answers both without computing a fee.
Q2.1
Savings: 30,000 × 1.0394 = $34,960.97 [1]. Term deposit: 30,000 × 1.0454 = $35,775.56 [2].
Q2.2
$35,775.56 − $34,960.97 = $814.59 [1].
Q2.3
The claim is true on one measure and unsupported on three [1]. Return: the term deposit does beat the savings account by $814.59, but shares and property are not in the comparison at all, so "best of the four" does not follow from a two-way calculation [1]. Risk: genuinely in its favour, since the term deposit is guaranteed and shares and property are not [1]. Liquidity: against it, and this is the one Priya has missed: the term deposit is locked for the full 4 years, making it less accessible than the savings account she rejected and than shares, which sell in days [1]. Cost to enter: in its favour, since it has none while shares cost brokerage twice and property carries stamp duty and fees. A complete answer: defensible for a fixed 4-year horizon with no tolerance for loss, but "best of the four" overstates a calculation that only compared two.