Mathematics • Year 10 • Unit 1 • Lesson 5
Financial Maths — Mixed Challenge
Pull together every idea from Unit 1 so far: pay (Lessons 1-2), budgets and GST (Lesson 3), discounts and mark-ups (Lesson 4) and simple interest (Lesson 5). Choose the right tool for each problem, spot someone else's mistake, then design a savings plan to hit a $5,000 goal.
1. Mixed problems — choose the right tool
Each question uses a different idea from Lessons 1-5. Decide which formula applies before you start writing. Show your working. 3 marks each
1.1 Find the simple interest on $6,500 at 4.2% p.a. for 18 months. (Lesson 5)
1.2 An investment earns $1,260 simple interest in 3 years at 6% p.a. Find the principal. (Lesson 5 — rearrangement)
1.3 A worker earns $32.80/hour for 38 normal hours plus 4 hours at time-and-a-half. Calculate gross weekly pay. (Lesson 2)
1.4 A retailer marks up shoes from a cost price of $48 by 75%, then sells them in a sale at 20% off. Find the sale price. (Lesson 4)
1.5 A printer is advertised as $440 (GST-inclusive). Find the GST charged and the pre-GST price. (Lesson 3)
1.6 Nina deposits her tax refund of $1,800 into a 6-month term deposit at 4.8% p.a. simple interest. Then she lets the matured total roll over into another 6-month deposit at the same rate. Find her total balance after 12 months. (Lesson 5)
2. Find the mistake
Another student has tried to calculate the simple interest on a $9,000 loan at 7.5% p.a. for 8 months. Their working is shown below. Exactly one line contains a mistake. Spot it, explain why it's wrong, then re-do the working correctly. 3 marks
Student's working — simple interest on $9,000 at 7.5% p.a. for 8 months:
Line 1: P = $9,000; R = 7.5% = 0.075; T = 8 months
Line 2: I = P × R × T = 9,000 × 0.075 × 8
Line 3: I = 9,000 × 0.075 × 8 = 675 × 8 = $5,400
Line 4: Total interest paid = $5,400.
(a) Which line contains the mistake?
(b) Explain in one or two sentences why that line is wrong.
(c) Write out the corrected working in full, including the corrected final answer.
Stuck? Look at Line 1 — T must be in years, not months, before you substitute. Eight months entered as "8" is treating the time as 8 years.3. Open-ended challenge — design a savings plan
This question has many valid answers. Be realistic, but show every number. 4 marks
3.1 You are saving up for a $5,000 overseas trip after Year 12. Design a savings plan that satisfies all of the following:
- You make a one-off lump-sum deposit into a term deposit (no monthly top-ups in this question).
- The deposit must mature into at least $5,000 in between 1 and 4 years.
- You choose a realistic Australian rate (between 3.5% and 5.5% p.a. simple interest).
- Your initial principal must be between $3,500 and $4,800.
Show:
(i) Your chosen principal (P), rate (R as a percentage and decimal) and time (T in years).
(ii) The simple interest earned (I = PRT).
(iii) The maturity amount (A = P + I).
(iv) A brief sentence saying whether your plan meets the $5,000 target and by how much.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Simple interest on $6,500 at 4.2% × 18 months
T = 18 ÷ 12 = 1.5 years. R = 0.042.
I = 6,500 × 0.042 × 1.5 = 273 × 1.5 = $409.50.
1.2 — Find the principal
P = I ÷ (R × T) = 1,260 ÷ (0.06 × 3) = 1,260 ÷ 0.18 = $7,000.
1.3 — Worker with overtime
Normal = 38 × $32.80 = $1,246.40.
Time-and-a-half rate = 1.5 × $32.80 = $49.20. Overtime pay = 4 × $49.20 = $196.80.
Total = $1,246.40 + $196.80 = $1,443.20.
1.4 — Mark-up then discount
Marked-up = $48 × 1.75 = $84.00.
Sale price = $84.00 × 0.80 = $67.20.
1.5 — Printer GST
GST = $440 ÷ 11 = $40.
Pre-GST = $440 − $40 = $400 (or $440 ÷ 1.10).
1.6 — Two rolled-over 6-month deposits
First 6 months: I = 1,800 × 0.048 × 0.5 = $43.20. Balance = $1,800 + $43.20 = $1,843.20.
Second 6 months (new principal = $1,843.20): I = 1,843.20 × 0.048 × 0.5 = $44.24 (approx).
Final balance after 12 months = $1,843.20 + $44.24 = $1,887.44.
Notice: rolling over isn't quite the same as one 12-month simple-interest deposit ($1,800 × 0.048 = $86.40 → balance $1,886.40). The roll-over earns slightly more because the second 6 months is interest on a slightly larger balance — a tiny taste of compounding, which is Lesson 6's main idea.
2 — Find the mistake
(a) The mistake is on Line 1 (the value of T), which then poisons Lines 2-4.
(b) The student left T as "8 months" instead of converting to years. The formula I = PRT requires T in years, so 8 months should become 8 ÷ 12 = 2/3 ≈ 0.667 years. Using T = 8 treats the time as 8 years and makes the answer about 12× too big.
(c) Corrected working:
T = 8 ÷ 12 = 2/3 years (≈ 0.6667).
I = 9,000 × 0.075 × (8 ÷ 12) = 675 × (8 ÷ 12) = 675 × 0.6667 = $450.00.
$450 is a much more believable figure for 8 months on a $9,000 loan at 7.5%.
3 — Open-ended challenge (sample savings plan)
Plan: deposit P = $4,500 into a term deposit at R = 4.5% p.a. simple interest for T = 3 years.
Step 1 — Rate as decimal: R = 0.045.
Step 2 — Interest earned: I = P × R × T = 4,500 × 0.045 × 3 = 202.50 × 3 = $607.50.
Step 3 — Maturity amount: A = P + I = $4,500 + $607.50 = $5,107.50.
Step 4 — Does it meet the $5,000 goal? Yes — it exceeds the goal by $107.50.
Other valid plans:
- P = $4,800, R = 4.0%, T = 1.5 years → I = $288, A = $5,088 ✓.
- P = $4,000, R = 5.5%, T = 4 years → I = $880, A = $4,880 ✗ (just misses — would need either higher P or longer T).
Marking: 1 for inputs in the required ranges; 1 for correct I from PRT; 1 for correct A; 1 for the conclusion sentence comparing A to $5,000. Any valid plan that hits the constraints earns full marks.