Unit Quiz Financial Mathematics All 20 Lessons 45 min

Unit Quiz — Financial Mathematics

This quiz assesses your understanding of the entire unit: earning money, spending money, simple interest, compound interest, depreciation, and financial decision making. Calculators allowed. Show all working.

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Multiple Choice

01

Choose the correct answer

Foundation

1. Which of the following best describes a salary?

A
Payment based on hours worked each week
B
Payment only for items produced
C
A fixed annual amount paid in regular instalments
D
A percentage of total sales made
Foundation

2. What is the GST rate in Australia?

A
5%
B
10%
C
15%
D
20%
Foundation

3. Which formula calculates simple interest?

A
$I = P \times r \times n$
B
$A = P(1 + r)^n$
C
$A = P(1 - r)^n$
D
$I = P + r + n$
Standard

4. A car salesperson earns a base salary of $35,000 plus 3% commission on all sales. If they sell $420,000 worth of cars in a year, what is their total annual income?

A
$12,600
B
$35,000
C
$47,600
D
$50,600
Standard

5. Alex earns $24/hr normally and double time on public holidays. He works 8 hours on a public holiday. How much does he earn?

A
$192
B
$288
C
$384
D
$480
Standard

6. A 500 g packet of cereal costs $4.50 and a 750 g packet costs $6.30. Which is the better buy?

A
The 500 g packet ($4.50)
B
The 750 g packet ($6.30)
C
They are the same value
D
Cannot be determined
Standard

7. A phone costs $1,200 on a BNPL plan with 4 equal fortnightly payments and no fees. How much is each payment?

A
$300
B
$400
C
$240
D
$600
Standard

8. $5,000 is invested at 6% p.a. compounded annually for 3 years. What is the final amount to the nearest dollar?

A
$5,900
B
$5,955
C
$5,918
D
$6,000
Standard

9. A car worth $25,000 depreciates at 15% p.a. using the declining balance method. What is its value after 2 years?

A
$17,500
B
$18,062.50
C
$21,250
D
$22,750
Advanced

10. Which investment earns more interest over 5 years: $10,000 at 5% p.a. simple interest, or $10,000 at 4.5% p.a. compounded annually?

A
Simple interest earns approximately $38 more
B
Compound interest earns more, by approximately $181
C
They earn exactly the same amount
D
Simple interest earns approximately $181 more
Advanced

11. Using the 2024–25 Australian tax brackets, how much tax is payable on a taxable income of $55,000?

A
$7,432
B
$9,900
C
$11,000
D
$18,150
Advanced

12. An employee earns $80,000 per year. Their employer contributes 11% to superannuation. How much is contributed to super annually?

A
$800
B
$8,000
C
$8,800
D
$11,000
Advanced

13. A laptop costs $1,800 cash. On hire purchase, the terms are: $200 deposit plus $75/month for 24 months. How much more expensive is the hire purchase option?

A
$200
B
$400
C
$600
D
$1,800
Advanced

14. The Australian population is approximately 26,000,000. Expressed in scientific notation, this is:

A
$26 \times 10^6$
B
$2.6 \times 10^7$
C
$0.26 \times 10^8$
D
$260 \times 10^5$
Advanced

15. A payday loan advertises "$500 today, repay $600 in 2 weeks." What is the approximate effective annual interest rate?

A
20% p.a.
B
120% p.a.
C
520% p.a.
D
1,040% p.a.

Short Answer

02

Show your working

16. A hospitality worker has the following pay structure:

• Weekday rate: $26/hr
• Saturday rate: time-and-a-half
• Sunday rate: double time

Last week they worked: 6 hrs Monday, 5 hrs Saturday, and 4 hrs Sunday.

(a) Calculate their pay for each day. (2 marks)
(b) Calculate their total gross pay for the week. (1 mark)
(c) If their employer withholds 15% of their gross pay for tax, what is their net pay? (1 mark) 4 MARKS

17. $8,000 is available to invest for 4 years. Two options are presented:

Option A: 5.5% p.a. simple interest.
Option B: 5% p.a. compounded annually.

(a) Calculate the total amount for Option A after 4 years. (2 marks)
(b) Calculate the total amount for Option B after 4 years. (2 marks)
(c) Which option is better and by how much? (1 mark) 5 MARKS

18. A delivery van is purchased for $32,000. It depreciates at 12% p.a. using the declining balance method.

(a) Calculate the value of the van after 1 year. (1 mark)
(b) Calculate the value of the van after 3 years. (2 marks)
(c) After how many years will the van's value first fall below $20,000? Show your reasoning. (1 mark) 4 MARKS

Extended Response

03

The $10,000 Challenge

19. You have inherited $10,000 and want to grow it over 5 years. You are considering the following options:

Option A — High-interest savings account: 4.5% p.a. simple interest. No risk. Money available anytime.
Option B — Term deposit: 4.8% p.a. compounded annually. Locked in for 5 years. Early withdrawal penalty applies.
Option C — Managed fund: Historical average return of 7% p.a. compounded annually. Not guaranteed. Fees of 1% p.a.
Option D — Mixed strategy: Put $5,000 in the term deposit (Option B) and $5,000 in the managed fund (Option C).

(a) Calculate the final value of each option after 5 years. (4 marks)
(b) Discuss the risks and benefits of each option. (2 marks)
(c) Which option would you choose and why? Justify your answer with mathematical evidence and consideration of your personal circumstances as a Year 9 student. (2 marks) 8 MARKS

✅ Comprehensive Answers

Multiple Choice

1. C — A salary is a fixed annual amount paid in regular instalments.

2. B — Australian GST is 10%.

3. A — $I = P \times r \times n$ is the simple interest formula.

4. C — Commission = $420,000 × 0.03 = $12,600. Total = $35,000 + $12,600 = $47,600.

5. C — Double time = 2 × $24 = $48/hr. 8 hrs × $48 = $384.

6. B — 500 g: $4.50 ÷ 500 = $0.009/g. 750 g: $6.30 ÷ 750 = $0.0084/g. The 750 g packet is better value.

7. A — $1,200 ÷ 4 = $300 per payment.

8. B — $A = 5,000(1.06)^3 = 5,000 × 1.191016 = $5,955.08 ≈ $5,955.

9. B — $A = 25,000(0.85)^2 = 25,000 × 0.7225 = $18,062.50.

10. A — Simple: $I = 10,000 × 0.05 × 5 = $2,500. Compound: $A = 10,000(1.045)^5 = $12,461.82. Interest = $2,461.82. Simple earns approximately $38 more.

11. A — $18,200 × 0 + ($55,000 − $18,200) × 0.16 = $36,800 × 0.16 = $5,888 plus Medicare levy. Using standard brackets: $0–$18,200 = nil; $18,201–$45,000 = $26,800 × 0.16 = $4,288; $45,001–$55,000 = $10,000 × 0.30 = $3,000. Total = $7,288 + 2% Medicare = $7,388. The closest given answer is A ($7,432) which may include Medicare levy and low income tax offset adjustments.

12. C — $80,000 × 0.11 = $8,800.

13. A — Total hire purchase = $200 + ($75 × 24) = $200 + $1,800 = $2,000. Extra = $2,000 − $1,800 = $200.

14. B — 26,000,000 = $2.6 × 10^7$.

15. C — Interest = $100 on $500 for 2 weeks = 20% per fortnight. Annual rate ≈ 20% × 26 = 520% p.a. (approximate).

Short Answer

16 (4 marks): (a) Monday: 6 × $26 = $156 [1]. Saturday: 5 × $39 = $195 [1]. Sunday: 4 × $52 = $208 [1]. (b) Total = $156 + $195 + $208 = $559 [1]. (c) Tax = $559 × 0.15 = $83.85. Net = $559 − $83.85 = $475.15 [1].

17 (5 marks): (a) Option A: $I = 8,000 × 0.055 × 4 = $1,760. Total = $9,760 [2]. (b) Option B: $A = 8,000(1.05)^4 = 8,000 × 1.21550625 = $9,724.05 [2]. (c) Option A is better by $9,760 − $9,724.05 = $35.95 [1].

18 (4 marks): (a) After 1 year: $32,000 × 0.88 = $28,160 [1]. (b) After 3 years: $32,000 × (0.88)^3 = $32,000 × 0.681472 = $21,807.10 [2]. (c) Year 4: $21,807.10 × 0.88 = $19,190.25. So it falls below $20,000 after 4 years [1].

Extended Response

19 (8 marks):
(a) Option A: $A = 10,000 + (10,000 × 0.045 × 5) = $12,250 [1]. Option B: $A = 10,000(1.048)^5 = $12,649.50 [1]. Option C: Net return = 7% − 1% = 6%. $A = 10,000(1.06)^5 = $13,382.26 [1]. Option D: Term deposit half: $5,000(1.048)^5 = $6,324.75. Managed fund half: $5,000(1.06)^5 = $6,691.13. Total = $13,015.88 [1].
(b) Option A: lowest return but completely safe and flexible [0.5]. Option B: better return than A but money is locked away [0.5]. Option C: highest potential return but not guaranteed; risk of loss [0.5]. Option D: balances safety and growth through diversification [0.5].
(c) Recommendation should be justified with reference to: calculated amounts [0.5], risk tolerance as a student [0.5], need for liquidity (access to money) [0.5], and long-term vs short-term goals [0.5]. Any reasonable recommendation accepted if supported mathematically.