Unit 1 Topic 1 Review — Consumer Arithmetic

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Review Questions

1. Q1 — GST calculations

   Fluency

   (a) An item costs $85.00 before GST. Find the price including 10% GST.

   (b) A television is marked $132.00 including GST. Find the pre-GST price.

2. Q2 — Percentage change

   Fluency

   (a) A house was bought for $420 000 and sold for $483 000. Find the percentage increase.

   (b) A television is marked down 15% from $1200. Find the sale price.

3. Q3 — Calculating wages with overtime

   Fluency

   Jasmine earns $24.60 per hour. She works 38 hours at the normal rate and 4 hours overtime at time-and-a-half. Calculate her weekly gross pay.

4. Q4 — Net income calculation

   Fluency

   Sam earns a salary of $68 000. His tax is $14 422 and superannuation is $6800.

   (a) Find total deductions.

   (b) Find net income.

   (c) Express net income as a percentage of gross income.

5. Q5 — Simple interest calculations

   Fluency

   $4500 is invested at 3.8% p.a. simple interest for 2.5 years.

   (a) Find the interest earned.

   (b) Find the total amount at the end of the investment.

   (c) What rate would produce $513 interest on the same principal over the same time?

6. Q6 — Simple interest vs compound interest

   Understanding

   $12 000 is invested at 6% p.a. for 5 years. Compare the final amounts under simple interest and compound interest (compounded annually). How much more does compound interest earn?

7. Q7 — Compound interest with monthly compounding

   Understanding

   $8000 is invested at 5.4% p.a. compounding monthly for 3 years.

   (a) Find the final amount.

   (b) Find the interest earned.

   (c) Find the effective annual rate (EAR).

8. Q8 — Finding the principal for a target amount

   Understanding

   How much must be invested at 4% p.a. compounding quarterly to accumulate $25 000 in 6 years?

9. Q9 — Comparing accounts using EAR

   Understanding

   Account A: 5.2% p.a. compounding annually. Account B: 5.0% p.a. compounding monthly.

   (a) Find the EAR for each account.

   (b) Which account is better?

   (c) For $15 000 invested over 4 years, how much more does the better account earn?

10. Q10 — Commission income

    Understanding

    James is a real estate agent who earns a base salary of $2000 per month plus 1.8% commission on all sales. In March he sold properties worth $1.2 million. Find his gross income for March.

11. Q11 — Loan comparison: simple vs compound

    Understanding

    An $18 000 loan is available on two options:

    Option A: 9% p.a. simple interest for 4 years.

    Option B: 8.4% p.a. compounding monthly for 4 years.

    Find the total repayment for each option. Which is cheaper, and by how much?

12. Q12 — Investment target: find the principal

    Problem Solving

    Sofia wants to have $40 000 in 8 years. She finds a term deposit paying 3.6% p.a. compounding quarterly. What principal must she invest today?

13. Q13 — Income tax calculation using tax brackets

    Problem Solving

    Tax brackets (simplified):

    • $0 – $18 200: Nil
    • $18 201 – $45 000: 19c per $1 over $18 200
    • $45 001 – $120 000: $5092 + 32.5c per $1 over $45 000

    Calculate the income tax payable on a taxable income of $72 000.

14. Q14 — Rule of 72 and doubling time

    Problem Solving

    Use the Rule of 72 to estimate the doubling time for investments earning: (a) 4% p.a., (b) 6% p.a., (c) 9% p.a.

    Then verify your answer for (b) using A = P(1.06)^t to confirm when $5000 first exceeds $10 000.

15. Q15 — Total career income with pay rises and overtime

    Problem Solving

    Maya works 40 hours per week at $32 per hour. After 2 years she gets a 5% pay rise; after another 2 years she gets another 5% rise. She also works 3 hours overtime at time-and-a-half every week throughout. Working 52 weeks per year, calculate her total income across all 4 years.