This checkpoint assesses your understanding of investing vs saving, superannuation, financial literacy, inflation, scientific notation and unit synthesis. It covers Lessons 16–20.
❓ Multiple Choice (10 questions)
1. An investment returns 6% p.a. and inflation is 2.5% p.a. What is the approximate real return?
2. Who pays the Super Guarantee contribution?
3. A salary of $60,000 with an SG rate of 11.5% produces an annual super contribution of:
4. $5,000 at 7% p.a. for 40 years is approximately how many times larger than $5,000 at 7% for 20 years?
5. A grocery bill of $200 with 3% annual inflation will be approximately how much after 5 years?
6. Write 0.000045 in scientific notation.
7. (2 × 10^6) × (4 × 10^3) =
8. Diversification in investing means:
9. $8,000 is invested at 5% p.a. compounded monthly for 5 years. Inflation is 2% p.a. What is the approximate real value?
10. A budget surplus is $300/week. Income rises 2% p.a. and costs rise 3.5% p.a. What is the approximate real surplus after 3 years?
✍ Short Answer (4 questions)
11. A person earns $50,000 per year.
(a) Calculate their annual super contribution at an SG rate of 11.5%. (1 mark)
(b) If that single year's contribution grows at 6.5% p.a., calculate its value after 35 years. (2 marks)
(c) Calculate the value after 15 years at the same rate. (2 marks)
(d) Calculate the difference between (b) and (c). (1 mark)6 MARKS
12. A person has $20,000 in super and is comparing two funds. Both have a gross return of 6% p.a.
Fund A: 1.2% p.a. fee.
Fund B: 0.5% p.a. fee.
(a) Calculate the net annual return for each fund. (1 mark)
(b) Calculate the balance of Fund A after 20 years. (2 marks)
(c) Calculate the balance of Fund B after 20 years. (2 marks)
(d) Calculate the difference in dollar terms. (1 mark)
(e) Explain why fee comparison is important when choosing a super fund. (1 mark)7 MARKS
13. An item cost $150 in 2020. Inflation averaged 3.2% per year for 4 years.
(a) Calculate the cost of the item in 2024. (2 marks)
(b) Wages rose 2.5% per year over the same period. By what percentage did the item become less affordable? (3 marks)
(c) If a household spent 30% of their income on housing in 2020, and housing costs rose 20% while wages rose 10% over 4 years, what percentage of income goes to housing in 2024? (3 marks)8 MARKS
14. Application:
(a) Australia's population is approximately 26,400,000. Write this in scientific notation. (1 mark)
(b) Australia's GDP is approximately $2.3 × 10^12. Calculate GDP per person. (2 marks)
(c) Round your answer to 2 significant figures. (1 mark)
(d) National debt is approximately $9.5 × 10^11. Calculate debt per person. (2 marks)
(e) Round to 2 significant figures. (1 mark)
(f) Explain one advantage of using scientific notation for national economic data. (1 mark)8 MARKS
1. B — Real return ≈ 6% − 2.5% = 3.5%.
2. B — Employers are legally required to pay the Super Guarantee on top of salary.
3. C — $60,000 × 0.115 = $6,900.
4. A — 40 years: $5,000 × 1.07^40 ≈ $74,872. 20 years: $5,000 × 1.07^20 ≈ $19,348. Ratio ≈ 3.87 ≈ 4 times.
5. C — $200 × (1.03)^5 = $200 × 1.15927 = $231.85 ≈ $232.
6. B — 0.000045 = 4.5 × 10^-5 (decimal moved 5 places right).
7. A — (2 × 4) × 10^(6+3) = 8 × 10^9.
8. B — Diversification means spreading across asset classes to reduce risk.
9. B — Nominal: $8,000 × (1 + 0.05/12)^60 = $8,000 × 1.28336 = $10,266.88. Real ≈ $8,000 × 1.03^5 = $8,000 × 1.15927 = $9,274.16 ≈ $9,270.
10. C — Real surplus ≈ $300 × (1.02/1.035)^3 = $300 × 0.9570 = $287.10 ≈ $287.
Q11 (6 marks): (a) $50,000 × 0.115 = $5,750 [1]. (b) $5,750 × (1.065)^35 = $5,750 × 9.0623 = $52,108.23 [2]. (c) $5,750 × (1.065)^15 = $5,750 × 2.5718 = $14,787.85 [2]. (d) Difference = $52,108.23 − $14,787.85 = $37,320.38 [1].
Q12 (7 marks): (a) Fund A: 6% − 1.2% = 4.8%. Fund B: 6% − 0.5% = 5.5% [1]. (b) $20,000 × (1.048)^20 = $20,000 × 2.55403 = $51,080.60 [2]. (c) $20,000 × (1.055)^20 = $20,000 × 2.91776 = $58,355.20 [2]. (d) Difference = $58,355.20 − $51,080.60 = $7,274.60 [1]. (e) Fees compound over decades. A 0.7% difference over 20 years costs thousands in lost retirement savings [1].
Q13 (8 marks): (a) $150 × (1.032)^4 = $150 × 1.13427 = $170.14 [2]. (b) Wage multiplier = 1.025^4 = 1.10381. Price multiplier = 1.032^4 = 1.13427. Relative change = 1.13427 / 1.10381 = 1.0276. 2.76% less affordable [3]. (c) 2020 housing = 30% of income. 2024 housing cost = 30% × 1.20 = 36% of original income. But income rose 10%, so new percentage = 36% / 1.10 = 32.73% [3].
Q14 (8 marks): (a) 2.64 × 10^7 [1]. (b) ($2.3 × 10^12) ÷ (2.64 × 10^7) = 0.8712 × 10^5 = $87,120 [2]. (c) $87,000 [1]. (d) ($9.5 × 10^11) ÷ (2.64 × 10^7) = 3.598 × 10^4 = $35,980 [2]. (e) $36,000 [1]. (f) Scientific notation makes very large numbers readable and enables quick comparison of scale and magnitude [1].
Tick when you have finished all questions and checked your answers.