Topic Review — Financial Mathematics

Mixed questions covering simple interest, compound interest, depreciation, appreciation, present value and inflation. Click each answer button to reveal the solution.

1. Simple interest. Fluency

   Find the interest earned (I) and the total amount (A) for P = $3500, r = 6% p.a., n = 4 years.

2. Compound interest — annual. Fluency

   Find A for P = $4000, r = 7% p.a. compound interest (annual), n = 8 years.

3. Compound interest — monthly. Fluency

   Find A for P = $2000, r = 9% p.a. compounded monthly, n = 3 years.

4. Straight-line depreciation. Fluency

   A machine is purchased for $12000 and depreciates by straight-line at 15% p.a. Find its value after 5 years.

5. Reducing balance depreciation. Fluency

   A vehicle purchased for $18000 depreciates at 20% p.a. reducing balance. Find its value after 4 years.

6. Appreciation. Fluency

   A house purchased for $250000 appreciates at 4% p.a. Find its value after 6 years.

7. Find the principal. Understanding

   A compound investment at 10% p.a. grows to $13310 after 3 years. Find the original principal P.

8. Inflation. Understanding

   A coffee costs $4.50 today. At 3% annual inflation, find its cost in 5 years.

9. Present value. Understanding

   You want $30000 in 8 years. An account earns 5% p.a. compound. How much must you invest today?

10. Simple vs compound interest. Understanding

    $6000 is invested for 6 years. Option A: 8% p.a. simple interest. Option B: 7% p.a. compound interest (annual).

    • (a) Find the final value of each option.
    • (b) Which is better after 6 years?

11. Loan growth. Problem Solving

    Ben borrows $15000 at 6% p.a. compound interest (annual) and makes no repayments for 5 years.

    • (a) Find the balance owing after 5 years.
    • (b) How much interest has accumulated?
    • (c) If the loan instead charged 6% p.a. simple interest, how much interest would accumulate over 5 years?
    • (d) How much extra does Ben owe because of compound vs simple interest?

12. Multi-step depreciation and appreciation. Problem Solving

    A car is purchased for $40000. It depreciates at 15% p.a. reducing balance for 3 years. A shortage of second-hand cars then causes its value to appreciate at 5% p.a. for 2 more years.

    • (a) Find the car’s value after the first 3 years.
    • (b) Find its value at the end of the full 5 years.
    • (c) What is the net change in value over the full 5 years?
    • (d) Would the owner have been better off if the car had simply depreciated at 15% p.a. reducing balance for all 5 years? Find that value to compare.