What is compound interest?Easy

The short answer: compound interest is interest earned on interest already earned. Simple interest pays on the original amount for ever; compounding pays on the amount as it now stands. Over a year the difference is trivial. Over thirty it is most of the outcome.

Why nobody's intuition handles it

People estimate growth as if it were a straight line, and compounding is not one. 100 growing at 7% is 107 after one year and 114 after two — not 114 because 7 was added twice, but because the second 7% was charged on 107. The gap between the straight line and the curve is small early and enormous late, which is why the whole effect feels like it arrives suddenly.

The consequence people miss: most of the money arrives in the last stretch. Half the final balance of a long investment is typically produced in its final third, which is exactly the period somebody who started late does not have.

The one piece of arithmetic worth memorising

Divide 72 by the growth rate to get roughly the years to double. At 6% a year, about twelve years. At 9%, about eight. It is accurate enough for anything you would do in your head, and it turns a rate into a timescale, which is the form the question usually arrives in.

The compound growth calculator on this site does the exact version, and the arithmetic drill generates rounds of this kind for practice.

Three things that change the answer more than the rate

1. Time. The most powerful input by a distance, and the only one nobody can add to later.
2. What is deducted. A fee compounds in exactly the same direction as the returns do — see below.
3. Inflation. A balance can grow every year and buy less. Why money is worth less even though it grew separates the nominal number from the real one, and the real one is the only one that buys anything.

What a one per cent charge actually removes

This is the calculation that changes how people think about fees. A charge taken annually is not taken from your return — it is taken from your balance, including from the growth of all previous years, so it compounds against you exactly as your returns compound for you. Over a few years it is small. Over thirty it removes something close to a quarter of the final balance for a single percentage point.

Costs and fees works the arithmetic through and what fees actually cost puts the numbers on it. There is a calculator for it too, because the number is more convincing when you produce it yourself.

The same machine, running backwards

Debt compounds identically and nobody finds it charming. A balance carrying interest that is not fully repaid grows on the same curve — which is why a credit card balance behaves so differently from a mortgage with a schedule that retires it. The variable that decides which of the two you have is whether the payment exceeds the interest, and by how much.

Where it appears in everything else here

• Discounting — compounding run in reverse, which is how a future amount is turned into a value today.
• Why a leveraged ETF loses over time — compounding applied to a daily multiple produces something that is not the multiple of the period.
• The arithmetic of drawdowns — a 50% fall needs a 100% rise, and the asymmetry is the same maths seen from the other side.

The one sentence to take away

Compounding means growth is charged on the total rather than on the original, so time matters more than rate, and anything deducted annually is deducted from the compounding too.