Compound Interest Explained (With Simple Examples)
Compound interest means earning on your earnings. See how it works with simple numbers, why time matters more than you think, and how the Rule of 72 gives you a quick estimate.
6 min read · Updated
Key takeaways
- Compounding means your growth starts earning growth of its own.
- Time is the biggest ingredient: the later years do most of the work.
- The Rule of 72 estimates how long money takes to double: 72 ÷ yearly rate.
- Compounding works against you too, with debt and with fees.
Compound interest is often described as “interest on interest.” It’s one of the most important ideas in personal finance, and you only need basic arithmetic to understand it.
Simple vs. compound
Imagine you put $1,000 somewhere that grows by 5% a year.
With simple interest, you’d earn 5% of the original $1,000 every year: $50, then another $50, and so on. After 10 years, you’d have $1,500.
With compound interest, each year’s 5% is calculated on the new, bigger balance:
| Year | Start of year | Growth (5%) | End of year |
|---|---|---|---|
| 1 | $1,000.00 | $50.00 | $1,050.00 |
| 2 | $1,050.00 | $52.50 | $1,102.50 |
| 3 | $1,102.50 | $55.13 | $1,157.63 |
The growth each year gets a little bigger, because last year’s growth is now earning too. After 10 years, you’d have about $1,629 instead of $1,500.
Time does the heavy lifting
The real magic shows up over long periods. Keep that same $1,000 growing at 5% a year:
- After 10 years: about $1,629
- After 20 years: about $2,653
- After 30 years: about $4,322
Notice the pattern: the first 10 years added about $629. The last 10 years added about $1,669, with no extra money put in. That’s why people say the best time to start was years ago, and the second-best time is now.
The Rule of 72
Want a quick estimate of how long it takes money to double? Divide 72 by the yearly growth rate.
- At 6% a year: 72 ÷ 6 = about 12 years to double.
- At 4% a year: 72 ÷ 4 = about 18 years.
- At 9% a year: 72 ÷ 9 = about 8 years.
It’s an approximation, but a surprisingly good one for everyday rates.
Compounding works both ways
The same math that helps savings grow makes debt grow too. Credit card balances often charge high interest that compounds, which is why an unpaid balance can snowball.
It also applies to fees. A fee charged every year on your whole balance compounds against you, which is why small differences in fund fees can add up to large amounts over decades (see ETFs vs index funds).
Investing isn’t a fixed rate
Savings accounts can pay a steady, stated rate. Investments like stocks don’t. They can grow in one year and fall in the next, so their long-term growth is uneven and never guaranteed. The examples above use a steady 5% to make the math clear, not to predict any real return.
Common questions
What’s the difference between APR and APY? APY (annual percentage yield) includes the effect of compounding during the year; APR (annual percentage rate) usually doesn’t. For savings, APY is the more useful number to compare.
How often does interest compound? It depends: daily, monthly or yearly are common. More frequent compounding grows slightly faster at the same stated rate.
The one thing to remember
Growth that earns growth needs time more than anything else. Starting earlier, even with less, often matters more than starting bigger later.
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