Simple & Compound Interest

• Interest is money added on top of an original amount — as a reward for saving, or a cost for borrowing.
• Simple interest is calculated on the starting amount only, every single time — so the interest payment never changes.
• Compound interest is calculated on the running total — so each year's interest is bigger than the last, because it's interest-on-interest.
• Both use a multiplier (like 1.04 for a 4% increase) to shortcut the working.
• Compound interest over several years can be written as one clean formula using powers: P × mn.
• Reverse problems ask you to work backwards — given the final amount, find the original, the rate, or the number of years.
• Depreciation is the exact same maths as compound interest, except the multiplier is less than 1 because the value is shrinking, not growing.

Imagine you lend your friend £100, and they agree to pay you back with 10% "simple" interest every year they keep it. Here's the key idea: that 10% is always calculated on the original £100 — never on anything bigger. So every single year, you earn exactly £10. Not £10, then £11, then £12.10 — always £10, flat, forever, because simple interest never looks at what's grown since the start; it only ever looks back at day one.

This is what "simple" means in the name — it's simple because the calculation never changes. Once you know the interest for one year, you know it for every year: just multiply by however many years have passed.

There are two things you might be asked for, and it's crucial not to mix them up:

• Total interest earned → find the percentage of the starting amount, then multiply by the number of years.
• Total balance (final amount) → do the above, then add it back onto the starting amount.