How compound interest works

Simple interest pays you on your money. Compound interest pays you on your money and on the interest it already earned. That one difference, repeated over years, is the most consequential piece of arithmetic in personal finance — and it runs in both directions.

The mechanic in one example

All numbers hypothetical. Put 1,000 at 5% simple interest and you earn 50 a year, every year: after 20 years, 1,000 + 20 × 50 = 2,000. Compound the same 5% and each year's interest joins the base for the next: 1,050 after one year, 1,102.50 after two — the extra 2.50 is interest on interest. After 20 years the total is about 2,653. Same rate, same deposit; the only change is that the interest was left in place.

Why time matters more than rate

Compounding is multiplication repeated, so its effect grows with the number of repetitions. Hypothetically, at 7% compounded yearly, money roughly doubles in a decade — and then that doubled amount doubles in the next one: 1,000 becomes about 2,000, then about 4,000, then about 8,000 over thirty years. Three decades did not add three times the growth of one decade; it added seven times. This is why an early start with a small amount so often ends ahead of a late start with a large one — the early money simply gets more doublings.

The rule of 72

A useful approximation: divide 72 by the yearly rate to estimate the years needed to double. At 6%, about 12 years; at 3%, about 24. It is an estimate, not a law — it drifts at extreme rates — but it turns any quoted rate into an intuition instantly.

The same arithmetic, pointed at you

Debt compounds by exactly the same rule. A balance carried on a credit card at a high rate grows on its interest the same way a deposit does — except you are on the paying side. Minimum payments that barely cover the month's interest leave the base nearly untouched, which is why such balances feel immovable: the arithmetic is working full-time for the lender.

What compounding cannot promise

Savings rates change, and investment returns are not a fixed rate at all — markets deliver uneven years, including negative ones, and past averages do not guarantee anything forward. Compounding describes how growth stacks when there is growth. Where returns come from in the first place is the subject of how people make money; what moves the rates themselves is in how interest rates affect markets.