Compound interest is a core topic in the GCSE Maths curriculum, appearing on all major UK exam boards (AQA, Edexcel, OCR). It's a real-world application of percentages that explains how money grows in savings accounts or how debts can increase. This guide will break it down clearly for both teachers and students.
What is Compound Interest?
Simple interest is calculated only on the original amount (the principal). Compound interest is different: interest is calculated on the principal and on any interest already earned. This means your money grows faster because you earn "interest on interest".
Think of it like a snowball rolling downhill, gathering more snow. Each time interest is added, the total amount gets bigger, so the next interest payment is calculated on a larger sum.
Key Terminology
Principal: The original amount of money invested or borrowed.
Interest Rate: The percentage increase, usually given per year (per annum).
Multiplier: The decimal you multiply by to apply the percentage change.
- Compounded: How often the interest is calculated and added (e.g., annually, monthly).
The Compound Interest Formula
You will need to know and apply this formula:
Total after (n) years = Principal (×) (Multiplier)(n)
Where the Multiplier is:
> 1 + (interest rate as a decimal)
For example, an interest rate of 5% gives a multiplier of 1.05.
This formula calculates the total amount (principal + all interest). To find just the interest earned, you subtract the original principal from this total.
Decision Flowchart: Which Method to Use?
When you see a compound interest problem, follow this logic:
flowchart TD
A["Start: Compound Interest Question"] --> B["Is it a
standard 'find total after n years'?"];
B -- Yes --> C["Use the formula:
Total = P × multiplier^n"];
B -- No --> D["Is it asking for
the interest only?"];
D -- Yes --> E["Calculate total first,
then subtract principal"];
D -- No --> F["Is the interest
compounded more than
once a year? e.g. monthly"];
F -- Yes --> G["Adjust rate and time:
Divide annual rate by periods,
Multiply years by periods"];
F -- No --> H["It may be a reverse
percentage question
'find original amount'"];
C --> I["Answer Found"];
E --> I;
G --> C;
H --> I;
Step-by-Step Walkthrough with Examples
Example 1: Standard Annual Compound Interest
"£800 is invested in a savings account for 3 years at 4% per annum compound interest. Calculate the total amount in the account after 3 years."
Identify the values:
Principal ((P)) = £800
Interest rate = 4%
Number of years ((n)) = 3
Multiplier = 1 + 0.04 = 1.04
- Apply the formula:
Total = P × multipliern
Total = 800 × (1.04)³
Calculate:
First, calculate (1.04³).
(1.04 × 1.04 = 1.0816)
(1.0816 × 1.04 = 1.124864)
Now, (800 × 1.124864 = 899.8912)
- State the answer clearly, in context and with correct rounding (usually to 2 decimal places for money):
> Total amount = £899.89
Example 2: Finding the Interest Only
Using the example above: "Calculate the interest earned."
You have already found the total: £899.89
- Subtract the original principal:
Interest = £899.89 - £800
Interest = £99.89
Example 3: Different Compounding Periods (Monthly)
"£500 is invested at an annual interest rate of 6%, compounded monthly. Find the value after 2 years."
Here, interest is added 12 times a year, not once. You must adjust the rate and the time.
Adjust the values:
Monthly interest rate = Annual rate ÷ 12 = 6% ÷ 12 = 0.5% per month.
As a decimal multiplier: 1 + (0.5100) = 1.005.
Number of time periods ((n)) = 2 years × 12 months = 24 months.
- Apply the formula with the new values:
Total = 500 × (1.005)²⁴
Calculate:
Use your calculator carefully: (500 × 1.005²⁴)
This equals (500 × 1.127159...)
- Which is £563.58 (to 2 d.p.)
Important: Always check if the question states an annual rate but compounds more frequently. This adjustment is a common exam trick!
Common Mistakes to Avoid
Using the simple interest method: Remember to raise the multiplier to the power of (n).
Incorrect multiplier: For a 5% decrease (like depreciation), the multiplier is 0.95, not 0.05.
Not adjusting for periods: For monthly compounding, using the annual rate and number of years in the formula will give a wrong answer.
- Rounding too early: Only round your final answer. Keep the full value of the multiplier power in your calculator.
Practice Question (Exam Style)
> Sarah invests £1,200 in a bond for 5 years.
> The bond pays compound interest at a rate of 3.2% per annum.
> Calculate how much more interest Sarah would get compared to if the bond paid simple interest at the same rate.
Worked Solution:
- Calculate Compound Interest Total:
Total_C = 1200 × (1.032)⁵
Total_C = 1200 × 1.1704...
Total_C = £1404.52
Interest_C = 1404.52 - 1200 = £204.52
Calculate Simple Interest Total:
Annual simple interest = 3.2% of £1200 = (0.032 × 1200 = £38.40)
Over 5 years = (38.40 × 5 = £192)
- Total with simple interest = (1200 + 192 = £1392)
Interest_S = £192
- Find the difference:
Difference = 204.52 - 192
Difference = £12.52
> Answer: Sarah would get £12.52 more interest with compound interest.
Summary and Exam Tips
Learn the formula: Total = Principal × (multiplier)n. Write it down at the start of the exam.
Check the compounding period. Is it annual, monthly, or quarterly?
Read the question carefully. Are you asked for the total or just the interest?
Use your calculator wisely. Use the power button (^ or (xy)) to calculate the multiplier to the power of (n) in one go.
- Link to other topics: Compound interest is closely related to percentage change and growth & decay problems (e.g., population growth).
- By mastering these steps, you'll be able to tackle any compound interest question that comes up in your GCSE Maths exam. Good luck!