Compound interest has been called the eighth wonder of the world, and the math backs the hype. It's the mechanism that turns modest, boring savings into serious wealth — or, when you're the one paying it, modest debts into heavy ones. One formula explains both.

Stacked coins growing along a rising curve into a plant

Simple vs. compound interest

Simple interest pays you only on your original deposit: $10,000 at 5% earns $500 every year, forever. Compound interest pays you on your deposit plus every dollar of interest you've already earned:

A = P × (1 + r/n)^(n·t)

• P — principal (starting amount)
• r — annual interest rate
• n — compounding periods per year
• t — years

$10,000 at 5%, compounded annually for 10 years, becomes $16,289 — not the $15,000 simple interest would give.

The rule of 72

Want a fast mental shortcut? The Rule of 72 says money doubles in roughly 72 ÷ interest rate years:

• 4% → doubles every ~18 years
• 6% → every ~12 years
• 9% → every ~8 years

At a long-run 7% stock market return, money doubles about every decade. Start at 25, and one dollar has doubled four times by 65 — it becomes sixteen.

The $100-a-month experiment

Compare two savers contributing $100/month at 7% annual return:

• Starts at 25, stops at 65: ~$265,000 from about $48,000 contributed
• Starts at 35, stops at 65: ~$122,000 from about $36,000 contributed

Ten years of delay costs $143,000 — more than triple the extra $12,000 contributed by the early saver. This is why "start early" is the most valuable sentence in personal finance: time does more of the work than money does.

Compounding frequency: the quiet bonus

The formula's n matters. The same 5% rate yields slightly more when compounded monthly or daily than once a year — banks quoting the same rate can deliver different effective returns. The difference on $10,000 over 10 years between annual and monthly compounding is a few hundred dollars; on mortgages and large portfolios, it's real money. The APY you see quoted already includes this effect, so compare APYs, not raw rates.

The dark side: compounding against you

The same force powers credit card debt at 20%+. A $5,000 balance with minimum payments takes decades to clear and can cost more in interest than the original purchases. Compound interest is symmetric: it magnifies whoever holds the position — saver or borrower.

Putting it to work

1. Automate contributions — time in the market beats timing.
2. Reinvest everything — dividends and interest are the fuel of compounding.
3. Kill high-rate debt first — a guaranteed 20% "return" by paying off a card beats any investment.
4. Be patient — the dramatic part of the curve only appears in the later years.

See the curve for yourself:

And when you're ready to borrow, read Loan Interest Explained to make sure compounding works for you, not against you.