Compound Intress

What Is Compound Interest?

Compound interest means earning interest not just on the original amount of money (the principal), but also on the interest that has already been added. This leads to faster growth than simple interest.

Formula for Compound Interest

The standard formula used is:

- Principal: the starting amount
- Rate: annual interest rate (as a percentage)
- Time: number of years
- Amount: total after interest is added

Example Question

Abdi invests £500 at 4% compound interest per year. Work out the total amount after 3 years.

Amount = 500 × (1 + 4/100)3
       = 500 × (1.04)3
       = 500 × 1.124864
       ≈ £562.43

Final Answer: £562.43

Key Tip

Always remember to:

• Convert percentages into decimals (e.g. 5% → 0.05 or 1.05)
• Use your calculator for accuracy, especially with powers
• Round your final answer to 2 decimal places, unless told otherwise

Common Mistakes to Avoid

• Confusing simple and compound interest
• Forgetting to add 1 to the interest rate before using powers
• Rounding too early — always round at the end

Practice Question

Sophie invests £800 in a savings account with a 3% annual compound interest rate. How much will she have after 4 years?

Try it yourself, then check with the formula:

Amount = 800 × (1 + 3/100)4
       = 800 × (1.03)4
       = 800 × 1.12550881
       ≈ £900.41

Answer: £900.41

Next Steps

• Practice with different interest rates and times
• Compare compound interest with simple interest to understand the difference
• Make sure you’re confident using a calculator for powers

Ready to Practise?

📝 Try the Compound Interest Quiz Now