Comparing investment strategies for HSC Maths Standard 2: savings accounts, term deposits, shares and property using compound growth, dividends and total return (Year 12 Investment and loans, 2024 syllabus)

Set up. Monthly rate $r = \frac{0.036}{12} = 0.003$ and $n = 5 \times 12 = 60$ periods.

Interest. $23\,937.90 - 20\,000 = \$3937.90$.

Rounding rule: calculate with the full calculator value and round to the nearest cent at the end. Marker's note: one mark for $r$ and $n$, one for the future value.

Compound

$FV = 20\,000 \times (1.042)^5 = \$24\,567.93$.

Simple

$I = Prn = 20\,000 \times 0.042 \times 5 = \$4200$, so the value is $\$24\,200.00$.

Compare

Compounding gives $24\,567.93 - 24\,200.00 = \$367.93$ more, because interest earns interest.

Marker's note: one mark for each value. Round at the end, to the nearest cent.

(a) Compare. The balances are $23 937.90 and $24 567.93, so the term deposit is larger by $630.04 (the difference of the unrounded balances $24,567.9314 and $23,937.8961, rounded to the cent).

(b) Reason. The savings account gives access to the money for emergencies or other opportunities, at a lower rate. A term deposit usually charges a penalty or refuses early withdrawal.

Marker's note: one mark for the two balances, one for the difference, one for a sensible reason.

(a) Cost

$800 \times 12.50 = \$10\,000$, plus $19.95, gives $10 019.95.

(b) Capital gain

Sale proceeds are $800 \times 14.10 - 19.95 = 11\,280 - 19.95 = \$11\,260.05$. Gain $= 11\,260.05 - 10\,019.95 = \$1240.10$.

(c) Dividends

$800 \times 0.46 \times 3 = \$1104$.

(d) Total return

$1240.10 + 1104 = \$2344.10$. As a percentage of the cost, $\frac{2344.10}{10\,019.95} \times 100 = 23.39\%$.

Marker's note: one mark for each part. The total return is the capital gain plus the dividends.

(a) Value

$650\,000 \times (1.035)^8 = \$855\,925.87$.

(b) Capital gain

$855\,925.87 - 650\,000 = \$205\,925.87$.

(c) Net rent

$14\,600 \times 8 = \$116\,800$.

(d) Total gain

$205\,925.87 + 116\,800 = \$322\,725.87$, which is $\frac{322\,725.87}{650\,000} \times 100 = 49.65\%$ of the purchase price.

Marker's note: one mark for each part. In practice, stamp duty, loan interest and selling costs would reduce this, which is why the question states the assumptions.

(a) Values.

• A: $30\,000 \times \left(1 + \frac{0.032}{12}\right)^{120} = \$41\,296$ (to the nearest dollar).
• B: $30\,000 \times 1.04^{10} = \$44\,407$.
• C: $30\,000 \times 1.065^{10} = \$56\,314$.

(b) With a fall. After $9$ years: $30\,000 \times 1.065^9 = \$52\,877$. A $20\%$ fall leaves $0.8 \times 52\,877.11 = \$42\,302$. This is below Option B's $44 407 by about $2106.

(c) Risk. The assumed average growth of shares is not guaranteed. Share prices can fall, so the final value can be less than a safe term deposit, while the term deposit's return is fixed in advance.

Marker's note: one mark for the three values, one for the year-$9$ value, one for the final value and comparison, one for the risk comment. Rounding rule: full calculator values, rounded at the end.