Full answer
Compound interest is the process of earning interest on interest. When interest is added to your principal balance and then that larger balance earns interest in the next period, the growth is exponential rather than linear. Albert Einstein allegedly called it "the eighth wonder of the world" — the quote is apocryphal, but the math behind it genuinely is remarkable over long time horizons.
A simple example: $10,000 invested at 7% annual return. With simple interest (no compounding), you earn $700 every year regardless — after 30 years you have $31,000. With annual compounding, Year 1 earns $700, Year 2 earns $749 (7% of $10,700), and so on — after 30 years the balance is approximately $76,123. The Rule of 72 gives a quick mental math shortcut: divide 72 by the interest rate to estimate how many years it takes to double. At 7%, money doubles every ~10 years.
Compounding frequency matters: accounts that compound daily (most high-yield savings accounts and money market funds) grow slightly faster than those compounding monthly or annually. The difference is minor at typical savings rates but becomes more meaningful at higher returns over longer periods.
The same principle works devastatingly against you with debt. A $5,000 credit card balance at 24% APR compounds monthly — you owe interest on interest if you don't pay in full. This is why minimum payment schedules are so damaging: the unpaid interest becomes principal, which then accrues more interest in a compounding spiral.
This is general information — consult a financial advisor for personalized investment guidance. The most powerful practical insight: starting to invest early matters far more than the amount, because time is the engine of compounding.