Pass an Exam 
Hi, I’m Ari. We can start simple interest from the beginning, work through an example together, or practise a question. Tell me which step is confusing.
GCSE Maths · Ratio & proportion
Simple interest GCSE Questions and Worked Answers
Simple interest is calculated on the original amount every year, so a fixed rate adds the same interest each year. Interest = principal × annual rate as a decimal × time in years. Add that interest to the principal to find the final balance.
Free AI tutor · GCSE simple interest
Practise GCSE simple interest for free with an AI tutor
Ask Ari for an explanation or work through an original exam-style question together.
AriYour maths coach
Chat cost ≈ $0.000000
Ari is an AI tutor and can make mistakes. Use the worked answers below to check important results.
Start with the meaning
What you need to know about simple interest
Suppose a savings model adds £20 each year to an original £400. After one year the balance is £420; after two it is £440. The yearly £20 is 5% of the original £400. When interest is always calculated from that original amount, it is called simple interest.
See the idea first
Equal additions, not repeated percentage growth
The original amount is called the principal, P. Let r be the annual rate written as a decimal, so 5% becomes 0.05. One year's interest is P × r. If that same payment is earned for t years, total interest I = P × r × t. The final balance is P + I; interest alone is not the balance.
| Year | Interest this year | Total balance |
|---|---|---|
| 0 | — | £400 |
| 1 | £20 | £420 |
| 2 | £20 | £440 |
| 3 | £20 | £460 |
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Find interest and balance
What the problem asks: £600 earns 4% simple interest for 3 years. Find both.
How to solve it: Each year adds 600 × 0.04 = £24. Three years add £72, giving a balance of £672.
Find the original amount
What the problem asks: A sum earns £90 simple interest in 3 years at 5% annually. Find the principal.
How to solve it: The total interest is 3 × 5% = 15% of the principal, so principal = 90 ÷ 0.15 = £600.
Find time or rate
What the problem asks: £500 earns £60 simple interest at 4% annually. How long does that take?
How to solve it: One year earns £20, so £60 takes 60 ÷ 20 = 3 years. Divide total interest by interest per year.
A reliable routine
Use the equal-yearly-interest model
Use this only when the problem specifies simple interest. The formula works because the rate is applied to the unchanged original principal each year; it does not model compound interest.
- Identify the original amount, annual rate and time.
- Convert the percentage rate to a decimal and time to years.
- Calculate yearly interest, then multiply by time; reverse these steps if an input is missing.
- Add the principal only if the question asks for the final balance.
Check: For part-years, this guide's questions explicitly assume interest is proportional to time. Real account terms may differ.
Fully worked
Simple interest GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
One year
Question
Find one year's simple interest on £750 at 4% annually.
The interest is £30. The final balance, if needed, would be £780.
Example 2
Several years
Question
£1200 earns 3% simple interest per year for 4 years. Find the final balance.
Yearly interest:
Total interest:
Balance:
The final balance is £1344.
Example 3
Time in months
Question
£800 earns 6% annual simple interest for 9 months, proportional to time. Find the interest.
Interest £36. Do not use 9 as the number of years.
Example 4
Recover the principal
Question
A sum earns £126 simple interest in 3 years at 7% annually. Find the sum invested.
The original sum was £600.
Example 5
Find an annual rate
Question
£900 earns £108 simple interest over 4 years. Find the annual percentage rate.
Yearly interest:
Rate as a decimal:
The annual percentage rate is 3%.
Example 6
Recover from a balance
Question
After 5 years at 4% annual simple interest, the balance is £1800. Find the original principal.
Total interest is 5 × 4% = 20% of the original. The balance is 120% of it.
Check: interest £300, balance £1800.
10 original questions · total 28 marks
Simple interest GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 33 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
Annual interest
Find one year's simple interest on £300 at 8% annually.
Show worked answer
Interest £24.
Three years
Find the simple interest on £500 at 6% annually for 3 years.
Show worked answer
Interest £90.
Final balance
Find the balance of £700 after 2 years at 5% annual simple interest.
Show worked answer
Balance £770.
Half a year
£1000 earns 4% annual simple interest for 6 months, proportional to time. Find the interest.
Show worked answer
Interest £20.
Eighteen months
£600 earns 8% annual simple interest for 18 months, proportional to time. Find the balance.
Show worked answer
Balance = £600 + £72 = £672.
Find time
£800 earns £120 simple interest at 5% annually. Find the time.
Show worked answer
Annual interest = 800 × 0.05 = £40.
Find rate
£400 earns £48 simple interest in 2 years. Find the annual percentage rate.
Show worked answer
Annual interest = £24.
Find principal
A principal earns £150 simple interest over 5 years at 3% annually. Find it.
Show worked answer
Principal £1000.
Balance versus interest
A balance grows from £200 to £230 in 3 years under simple interest. Find the annual percentage rate.
Show worked answer
Total interest = 230 − 200 = £30; yearly interest = £10.
Do not treat the whole £230 as interest.
Compare the models
Compare balances after 2 years for £100 at 10% annually under simple interest and under compound interest.
Show worked answer
Simple adds £10 each year: balance £120. Compound multiplies the updated balance:
Compound gives £121 because year 2 earns interest on £110, not £100.
Examiner-style feedback
Common simple interest mistakes
Simple interest always uses the original principal.
Convert a percentage into a decimal before multiplying.
Subtract the principal from a balance before working backwards from the interest.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
- Same principal each year.
- Annual rate and time units must match.
- Interest is P × r × t.
- Balance adds the original back.
Quick answers
Simple interest FAQ
Is simple interest the same as compound interest?
No. Compound interest uses an updated balance; simple interest keeps using the original principal.
What does per annum mean?
Per year. If the time is given in months, convert it to years before using an annual rate.
Content standards
Curriculum and rights review
R9 simple-interest calculations across tiers. All financial situations are simplified mathematical models, not product comparisons or financial advice. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
Official specification references