Short answer
Hire purchase lets you buy goods immediately and pay in instalments over time — but you always pay more than the cash price. GCSE maths questions ask you to calculate the total repayment, find the extra cost, or compare two credit deals. The key is to add up every payment carefully and subtract the cash price.
At a glance
- Key stage
- GCSE
- Subject
- Number
- Type
- Guide
- For
- Students
- Read time
- 5 min
- Last updated
- 21 October 2026
Where this fits
- Key Stage 3Years 7–9
- GCSEYears 10–11This article
What is hire purchase?
Hire purchase (HP) is a credit agreement where you pay a deposit upfront and then make regular monthly instalments until the full amount — including interest — is paid off. You do not own the item until the final payment is made.
A typical HP deal has three components:
| Component | Meaning |
|---|---|
| Deposit | Percentage or fixed amount paid immediately |
| Monthly instalment | Fixed payment each month |
| Number of months | How long the agreement lasts |
The cash price is what the item costs if bought outright. The total HP cost is always greater than the cash price; the difference is the extra cost of borrowing.
How do you calculate the total cost of a hire purchase agreement?
Add the deposit to the total of all monthly payments.
Total HP cost = deposit + (monthly instalment × number of months)
Worked example 1: A laptop has a cash price of £800. Under HP, the deposit is £120 and there are 24 monthly payments of £32. Find the total HP cost and the extra amount paid.
- Total HP cost = £120 + (24 × £32) = £120 + £768 = £888
- Extra cost = £888 − £800 = £88
Worked example 2: A television has a cash price of £600. HP requires a 15% deposit and 18 monthly payments of £35.
- Deposit = 15% of £600 = 0.15 × £600 = £90
- Total HP cost = £90 + (18 × £35) = £90 + £630 = £720
- Extra cost = £720 − £600 = £120
Always check your answer is greater than the cash price — if it is not, you have made an error.
How do you find a missing instalment or number of months?
Sometimes the question gives you the total HP cost and asks for a missing value. Rearrange the formula.
Worked example: Total HP cost is £1 080. The deposit was £180 and there were 12 monthly payments. Find each payment.
- Total instalments = £1 080 − £180 = £900
- Monthly payment = £900 ÷ 12 = £75
Worked example: Deposit = 20% of £950 = £190. Monthly payment = £60. Total HP cost = £730. Find the number of months.
- Total instalments = £730 − £190 = £540
- Number of months = £540 ÷ £60 = 9 months
How do you compare two credit deals?
Calculate the total cost of each deal separately, then subtract.
Worked example: Maya wants to buy a sofa priced at £1 200.
- Deal A: 10% deposit, then 24 payments of £52.
- Deal B: No deposit, then 30 payments of £44.
Deal A total = 10% × £1 200 + 24 × £52 = £120 + £1 248 = £1 368
Deal B total = 0 + 30 × £44 = £1 320
Deal B costs £48 less overall, so it is the better deal on total repayment — even though the monthly amount is less.
Note: Deal B lasts 30 months vs 24 months for Deal A. Questions may ask you to comment on this — a longer commitment can be a disadvantage even if the total is lower.
What is APR and does it appear at GCSE?
APR (Annual Percentage Rate) is a standardised way of expressing the yearly cost of credit, including fees and interest. At GCSE you are not expected to calculate APR from scratch, but you may be asked to use it in a sentence: "APR 29.9% means you are charged an effective annual rate of 29.9% on the outstanding balance."
A higher APR means a more expensive deal. However, exam questions almost always compare deals using total repayment cost rather than APR, so practise the total-cost method.
What percentage of the cash price is the extra cost?
Some questions ask for the extra cost as a percentage of the cash price.
Formula: percentage extra = (extra cost ÷ cash price) × 100
Example: Cash price £600, total HP £720, extra cost £120.
Percentage extra = (120 ÷ 600) × 100 = 20%
What do GCSE exam questions on hire purchase look like?
| Question type | What to do |
|---|---|
| "Find the total cost" | Deposit + (monthly × months) |
| "Find the extra cost" | Total HP − cash price |
| "Express extra cost as %" | (extra ÷ cash price) × 100 |
| "Find missing instalment" | Rearrange formula |
| "Which deal is cheaper?" | Calculate total for each; compare |
| "Comment on the deals" | Compare total cost AND length of agreement |
Always show your working in full — method marks are available even if your final answer is wrong.
Frequently asked questions
Does the deposit always reduce the total amount I repay?
No — the deposit is part of the total HP cost, not a separate saving. A larger deposit usually means smaller monthly payments but does not necessarily mean a lower total repayment. Always calculate the full total before deciding which deal is better.
What if the deposit is given as a fraction instead of a percentage?
Work it out in the same way. For example, a deposit of one fifth of £480 = £480 ÷ 5 = £96. Then add the monthly payments as normal. Treat "one tenth" and "10%" as identical — both give you the same value.
Can the total HP cost ever equal the cash price?
In practice, never — the lender charges interest and fees. However, some exam questions use 0% interest (so total HP equals cash price) to test arithmetic skills or to contrast with a second deal that does charge interest. Read the question carefully.
Why do GCSE questions include hire purchase?
Hire purchase is part of the financial maths strand of the GCSE specification. It appears alongside simple interest, compound interest, percentage increase and decrease, and currency exchange — all situations where you must apply percentages and arithmetic in a real-world context.
Professor Pi walks you through every financial maths question step by step — add the AI Tutors connector at aitutors.me.
Key terms
- Hire purchase (HP)
- deposit
- monthly instalments
- cash price
- total HP cost
- total cost
- Deal A
- Deal B