• 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.

This is the concept that trips people up the most, so let's be really precise about it. With compound interest, each year's interest is calculated on the current balance — meaning last year's interest earns interest too. It's a snowball: the more it grows, the faster it grows.

Watch what happens to $100 at 10% interest each year, for 3 years, and compare the two methods side by side:

Notice the compound column earns a little more each year — $10, then $11, then $12.10 — because the base it's calculated from keeps growing. That extra $3.10 compared to simple interest ($133.10 vs $130) is entirely "interest on interest."

Doing the year-by-year table works, but it's slow for anything beyond 3 or 4 years. Here's the shortcut: since you're multiplying by the same multiplier every single year, that's just repeated multiplication — which is exactly what powers (indices) are for.

To increase $300 by 5% once: 300 × 1.05. To do it again the next year: (300 × 1.05) × 1.05 = 300 × 1.05². Do it a third time and it becomes 300 × 1.05³. The power is simply "how many years."

Sometimes a bank offers, say, 3% for the first two years and then 2% for the year after. Don't panic — you simply treat each rate period as its own separate calculation, feeding the result of the first period in as the starting amount for the next.

Sometimes you're given the final balance and asked to find the original amount, the rate, or the time. The trick is simple: since Final = P × mn, you just rearrange by dividing.

Depreciation is the mirror image of compound interest. Instead of a value growing by a percentage each year (like a savings account), a value shrinks by a percentage each year (like a car or a phone losing resale value). The maths is identical to compound interest — you still raise a multiplier to a power — the only difference is the multiplier is now less than 1, because you're keeping a smaller percentage each time, not adding more on top.

Find the multiplier by subtracting the percentage decrease from 100%. A 15% depreciation means you keep 85% of the value each year, so the multiplier is 0.85 (not 1.15 — that would be growth, the opposite of what's happening).

• I can explain the difference between simple and compound interest in my own words.
• I can calculate total simple interest earned over n years.
• I can find the final balance after simple interest (not just the interest itself).
• I can convert a percentage rate into a multiplier for both increases and decreases.
• I can apply the compound interest formula P × (1 + r/100)ⁿ correctly.
• I remember that this formula gives the TOTAL BALANCE, and I subtract P if asked for interest only.
• I can handle problems where the interest rate changes partway through the investment.
• I can solve reverse compound interest problems to find the original amount, P.
• I understand depreciation uses the same method as compound interest, but with (1 − r/100).
• I can find "amount lost" in a depreciation problem by subtracting final value from original value.
• I know neither formula is given to me in the exam — I have them memorised.