Compound interest
When interest gets added to your balance, then earns interest itself.
Compound interest is interest that earns interest. If you put $1,000 in an account that pays 5% per year and never touch it, after one year you have $1,050. After two years you don't have $1,100 — you have $1,102.50, because the second year's 5% was calculated on the new balance, not the original.
It sounds like a small detail. Over 30 years it's the difference between a comfortable retirement and a panicked one.
The math: future balance ≈ principal × (1 + rate)^years. The exponent is what does the work. Time matters more than the rate, which is why "start early" is the most repeated advice in personal finance — and the most ignored.
Example
$10,000 invested at 8% per year becomes $46,610 after 20 years — most of that is interest earning interest.
Why this matters
It's the only force that lets ordinary savings build real wealth over time. It's also the force that makes credit-card debt cost so much more than people think.
The catch
Compound interest works for you on the way up and against you on the way down. The same math that grows a 401(k) over 30 years grows credit-card debt over 30 months — just faster, because the rate is higher.