Understanding how money grows over time is crucial for making...
Maths420 views·Updated 29 Jul 2026·3 pagesUnderstanding Compound and Simple Interest: Revision Notes
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Compound Interest Basics
Ever wondered how your savings account balance seems to grow faster each year? That's compound interest at work – it's literally money making money!
Unlike simple interest, compound interest doesn't just calculate earnings on your original amount. Instead, it calculates interest on your original money PLUS all the interest you've already earned. This creates a snowball effect that makes your money grow exponentially.
The formula is: Amount = Principal × Multiplier^n (where n = number of time periods). The multiplier is simply 1 + the interest rate as a decimal. So if you have 6% interest, your multiplier becomes 1.06 – the "1" represents your original money, and the "0.06" is the additional 6% you're earning.
Quick Tip: Always convert percentages to decimals first, then add 1 to get your multiplier!
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of 3
Compound Interest Example
Let's see compound interest in action with Sally's £1500 at 6% interest over 3 years. First, convert 6% to 0.06, then add 1 to get the multiplier of 1.06.
The calculation becomes: £1500 × 1.06³ = £1786.52. Notice how we raise 1.06 to the power of 3 because the money compounds for 3 years.
Here's what's brilliant about this: each year, Sally earns interest not just on her original £1500, but on all the interest from previous years too. Year 1 she earns interest on £1500, but by year 3 she's earning interest on over £1685!
Remember: The power (exponent) always equals the number of time periods your money is invested.
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Simple Interest Made Simple
Simple interest is much more straightforward – you only ever earn interest on your original investment amount, never on the interest itself. Think of it as a flat rate that never changes.
Using Aleesha's example: £1000 at 5% simple interest for 2 years. The method shown breaks it down: find 1% of £1000 (which is £10), then multiply by the interest rate (5 × £10 = £50 per year), then multiply by the number of years (£50 × 2 = £100 total interest).
So Aleesha gets her original £1000 back plus £100 interest, making £1100 total. With simple interest, she'd earn exactly £50 every single year – no more, no less.
Key Difference: Simple interest = same amount each year. Compound interest = increasing amount each year!
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Maths420 views·Updated 29 Jul 2026·3 pagesUnderstanding Compound and Simple Interest: Revision Notes
Understanding how money grows over time is crucial for making smart financial decisions. There are two main ways interest works: compound interest (where your interest earns more interest) and simple interest (where only your original amount earns interest).
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Compound Interest Basics
Ever wondered how your savings account balance seems to grow faster each year? That's compound interest at work – it's literally money making money!
Unlike simple interest, compound interest doesn't just calculate earnings on your original amount. Instead, it calculates interest on your original money PLUS all the interest you've already earned. This creates a snowball effect that makes your money grow exponentially.
The formula is: Amount = Principal × Multiplier^n (where n = number of time periods). The multiplier is simply 1 + the interest rate as a decimal. So if you have 6% interest, your multiplier becomes 1.06 – the "1" represents your original money, and the "0.06" is the additional 6% you're earning.
Quick Tip: Always convert percentages to decimals first, then add 1 to get your multiplier!
2
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Compound Interest Example
Let's see compound interest in action with Sally's £1500 at 6% interest over 3 years. First, convert 6% to 0.06, then add 1 to get the multiplier of 1.06.
The calculation becomes: £1500 × 1.06³ = £1786.52. Notice how we raise 1.06 to the power of 3 because the money compounds for 3 years.
Here's what's brilliant about this: each year, Sally earns interest not just on her original £1500, but on all the interest from previous years too. Year 1 she earns interest on £1500, but by year 3 she's earning interest on over £1685!
Remember: The power (exponent) always equals the number of time periods your money is invested.
3
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- Improve your grades
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By signing up you accept Terms of Service and Privacy Policy
Simple Interest Made Simple
Simple interest is much more straightforward – you only ever earn interest on your original investment amount, never on the interest itself. Think of it as a flat rate that never changes.
Using Aleesha's example: £1000 at 5% simple interest for 2 years. The method shown breaks it down: find 1% of £1000 (which is £10), then multiply by the interest rate (5 × £10 = £50 per year), then multiply by the number of years (£50 × 2 = £100 total interest).
So Aleesha gets her original £1000 back plus £100 interest, making £1100 total. With simple interest, she'd earn exactly £50 every single year – no more, no less.
Key Difference: Simple interest = same amount each year. Compound interest = increasing amount each year!
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