The Core Idea
With simple interest, you earn interest only on your original deposit. With compound interest, you earn interest on your original deposit plus on all the interest you've already accumulated. That distinction sounds subtle, but over long time horizons it creates a massive difference in wealth.
"Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn't, pays it." — often attributed to Albert Einstein
A Simple Example: Year by Year
You invest $10,000 at a 5% annual rate, compounded annually. Watch what happens each year:
| Year | Opening Balance | Interest Earned | Closing Balance |
|---|---|---|---|
| 1 | $10,000.00 | $500.00 | $10,500.00 |
| 2 | $10,500.00 | $525.00 | $11,025.00 |
| 3 | $11,025.00 | $551.25 | $11,576.25 |
| 4 | $11,576.25 | $578.81 | $12,155.06 |
| 5 | $12,155.06 | $607.75 | $12,762.82 |
| 10 | — | — | $16,288.95 |
| 20 | — | — | $26,532.98 |
| 30 | — | — | $43,219.42 |
Notice that the interest earned increases every year even though you added no new money. In Year 1 you earned $500; by Year 5 you're earning over $607 on the same deposit. This acceleration is the compounding effect.
Compound vs Simple Interest: The Key Difference
Over the same 30-year period at 5%, simple interest would give you $10,000 + (5% × $10,000 × 30) = $25,000. Compound interest delivers $43,219 — a 73% better outcome from the same original deposit.
See the full simple vs compound interest comparison →
How Compounding Frequency Affects Your Returns
The formula for compound interest is A = P(1 + r/n)^(nt), where n is how many times per year interest is compounded. The more frequently it compounds, the more you earn — though the gains from daily vs monthly are modest.
| Compounding | $10,000 after 20 yrs @ 5% | Difference vs Annual |
|---|---|---|
| Annual (n=1) | $26,532.98 | — |
| Quarterly (n=4) | $26,850.64 | +$317.66 |
| Monthly (n=12) | $27,126.44 | +$593.46 |
| Daily (n=365) | $27,179.22 | +$646.24 |
| Continuous | $27,182.82 | +$649.84 |
Where You Encounter Compound Interest
Working for you (savings & investments)
- High-yield savings accounts — banks typically compound daily or monthly
- Certificates of deposit (CDs) — fixed rate, often compounded daily
- Roth IRA and 401(k) accounts — investment returns compound over decades
- Stock market index funds — dividend reinvestment creates compounding
- Money market accounts — competitive rates with frequent compounding
Working against you (debt)
- Credit card debt — typically compounded daily at 20%+ APR, very costly
- Student loans — interest capitalizes (compounds) if you defer payments
- Mortgage interest — while amortized monthly, unpaid interest capitalizes
The same compounding that grows your savings also accelerates debt. A $5,000 credit card balance at 22% APR compounds to nearly $45,000 in 10 years with no payments.
The Rule of 72
A quick mental math trick: divide 72 by your annual interest rate to estimate how many years it takes to double your money.
- At 4%: 72 ÷ 4 = 18 years to double
- At 6%: 72 ÷ 6 = 12 years to double
- At 8%: 72 ÷ 8 = 9 years to double
- At 12%: 72 ÷ 12 = 6 years to double