Earning interest on your interest is how small savings become large ones. Here's the mechanism, in plain terms.
Simple interest pays only on your original deposit. Compound interest pays on your deposit and on the interest you've already earned. Each period, your balance is a little bigger, so the next interest payment is a little bigger too — and the effect snowballs over time.
The future value is A = P(1 + r/n)nt, where P is the principal, r is the annual rate, n is how many times it compounds per year, and t is years. Add regular contributions and the growth accelerates further.
Put $10,000 in at 7% compounded monthly for 30 years and it grows to about $81,000 — without adding a cent. Contribute $200 a month on top and you'd finish near $325,000, of which only about $82,000 is money you put in. The rest is compounding.
Want a quick estimate of how long it takes to double your money? Divide 72 by your interest rate. At 6%, money doubles in about 12 years; at 9%, about 8 years. It's a handy mental shortcut for rates between roughly 4% and 12%.
Because compounding builds on itself, time is its most powerful ingredient. A saver who starts at 25 can end up with far more than someone who starts at 35 and contributes more — simply because the early money had more years to compound.