Learning Objectives
- identify cash price, deposit and instalments;
- calculate total hire-purchase cost;
- calculate the extra amount paid above cash price;
- compare payment plans;
- solve reverse hire-purchase problems.
Introduction
This lesson develops Hire Purchase and Instalments from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Notice→Connect→Explain
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
🌍 Where Will You Use This?
Hire purchase is used when an item is taken immediately but paid for over time through a deposit and instalments.
The Structure of Hire Purchase
Total HP Cost = Deposit + (Number of Instalments × Instalment Amount)
Worked Example 1
A television has a cash price of US$600. Under hire purchase, a deposit of US$120 is paid followed by 18 monthly instalments of US$32.
1
Total instalments = 18×32 = US$576.
2
Total HP cost = 120+576 = US$696.
3
Extra paid = 696−600 = US$96.
Percentage Extra Paid
Extra percentage = Extra paid ÷ Cash price × 100%
Using the television example:
Extra percentage = 96÷600×100 = 16%.
Reverse Problem
Total HP cost is US$1,040. The deposit is US$200 and there are 24 equal instalments. Find each instalment.
1
Total instalments = 1040−200 = US$840.
2
Each instalment = 840÷24 = US$35.
Comparing Two Plans
Plan A: US$100 deposit + 12 payments of US$48.
Plan B: US$160 deposit + 10 payments of US$50.
Plan A total = 100+12×48 = US$676.
Plan B total = 160+10×50 = US$660.
Plan B is cheaper by US$16.
💼 Money Smart Tip
A lower monthly instalment does not always mean a cheaper plan. Compare the total amount paid.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- A fridge requires US$150 deposit and 20 payments of US$28. Find the total HP cost.
- The cash price is US$620 and HP total is US$744. Find the extra paid.
- A deposit of US$90 and 15 instalments produce a total cost of US$540. Find each instalment.
- A laptop cash price is US$800. HP terms are 25% deposit and 18 payments of US$39. Find total HP cost and extra percentage.
- Compare:
- US$120 deposit + 24×US$30;
- US$200 deposit + 18×US$36.
- A cash price is US$900. Under HP, a 20% deposit is followed by equal monthly instalments for 2 years. The customer pays 18% more than the cash price in total. Find each monthly instalment.
✅ Check Your Work
Show practice answers
- 150+20×28 = US$710.
- US$124.
- (540−90)÷15 = US$30.
-
Deposit=200; instalments=18×39=702; total=US$902.
Extra=102; extra percentage=12.75%. -
Plan A=120+720=US$840.
Plan B=200+648=US$848.
Plan A is cheaper by US$8. -
Total HP=900×1.18=US$1,062.
Deposit=US$180.
Instalments total=882.
Monthly instalment=882÷24=US$36.75.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Total HP cost = deposit + all instalments.
- Extra paid = HP total − cash price.
- Compare total costs, not only monthly payments.
- Reverse problems often require subtracting the deposit first.