Practice Maths

Topic Review — Financial Mathematics

Mixed Practice — L05 – L07

This review covers percentages and financial applications, simple interest, and compound interest. Try each question before checking your answers.

Review Questions

  1. Percentage increases, decreases, and reverses. Fluency

    1. Increase $480 by 15%.
    2. Decrease $750 by 20%.
    3. After a 25% increase, a price is $375. Find the original price.
    4. A jacket sells for $136 after a 15% discount. Find the original price.
    5. A laptop costs $1650 including 10% GST. Find the pre-GST price and the GST component.

  2. Simple interest calculations. Fluency

    1. Find the simple interest: P = $5000, R = 6% p.a., T = 3 years.
    2. Find the total amount: P = $3500, R = 4% p.a., T = 4 years.
    3. Find the rate: I = $720, P = $4000, T = 3 years.
    4. Find the time: I = $1050, P = $7000, R = 5% p.a.
    5. Find the principal: I = $540, R = 4.5% p.a., T = 4 years.

  3. Compound interest and depreciation. Fluency

    1. Find A: P = $4000, r = 5% p.a., n = 3 years (annual compounding).
    2. Find A: P = $9000, r = 3.5% p.a., n = 4 years.
    3. Find the compound interest earned: P = $6000, r = 4% p.a., n = 5 years.
    4. A motorbike worth $12 000 depreciates at 14% p.a. for 4 years. Find its value after 4 years.
    5. A computer bought for $3500 depreciates at 25% p.a. Find its value after 3 years.

  4. Multi-step financial problems. Understanding

    1. A price increases by 10% in Year 1, then decreases by 10% in Year 2. Is the final price the same as the original? Explain with a $400 example.
    2. Compare: investing $8000 at 5% p.a. simple interest for 4 years versus 5% p.a. compound interest for 4 years. Which earns more? By how much?
    3. A tradesperson charges $680 + GST. A student pays this bill using their $750 savings. How much change do they receive?
    4. An agent earns 2.5% commission. If they earn $3750 commission in a month, what were their total sales?
    5. A trader buys 50 items at $24 each and sells 45 at $36 each. The remaining 5 are sold at a 50% discount on the selling price. Find the overall profit percentage on cost.

  5. Problem solving — choosing the right financial tool. Problem Solving

    1. Lena has $20 000 to invest for 5 years. She is comparing:
      • Option A: 7% p.a. simple interest
      • Option B: 6% p.a. compound interest (annual)
      • Option C: 5.5% p.a. compound interest (annual)
      Rank the options from highest to lowest total amount. Show all working.
    2. A car is purchased new for $38 000. It depreciates at 15% p.a. A buyer says: “After 5 years the car has lost 75% of its value.” Is this correct? Calculate the actual depreciated value and percentage loss.
    3. A home loan of $350 000 is offered at 4.8% p.a. simple interest over 20 years.
      1. Find the total amount repaid.
      2. Find the monthly repayment.
      3. Comment on whether simple interest is realistic for a mortgage and what difference compound interest would make.
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