Compound Interest Definition: Compound interest is interest calculated on both the original sum and on all the interest that has already been added to it. Because each period’s interest becomes part of the base for the next period, the balance grows faster every year, so $10,000 at 7% a year becomes about $76,000 after 30 years instead of the $31,000 that simple interest would produce. The same mechanism works against borrowers, making unpaid debt grow at an accelerating pace.
What Is Compound Interest?
Put $1,000 in an account paying 10% a year. After the first year you have $1,100. In the second year you earn 10% on $1,100, not on $1,000, so you receive $110 instead of $100, and that extra $10 is compounding at work.
Simple interest pays only on the original amount, called the principal. Compound interest adds each payment to the principal, so the next payment is calculated on a bigger number. In the early years the difference looks trivial, but the gap widens every period because the growth feeds on itself.
This is why time matters more than the starting sum. A saver who begins 10 years earlier often ends up with more than one who invests twice as much later. To see how large the effect becomes, you need the formula.
How Does Compound Interest Work?
The standard formula is A = P × (1 + r/n)^(n × t). Here A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is how many times per year interest is added, and t is the number of years.
Take $10,000 at 7%, compounded once a year. After 10 years it grows to about $19,700, and after 20 years to about $38,700. After 30 years it reaches roughly $76,100, so the last decade adds more than the first two combined.
Simple interest on the same $10,000 pays a flat $700 a year, or $21,000 over 30 years, for a total of $31,000. The $45,000 difference comes entirely from interest earning interest. That is the gap you give up by withdrawing earnings instead of leaving them to grow.
Compounding frequency adds a smaller boost. At 12% a year compounded monthly, each month adds 1%, and $10,000 becomes about $11,268 after one year rather than $11,200. The effective annual return of 12.68% is what the annual percentage yield measures, while the 12% headline figure is the annual percentage rate.
The Rule of 72
You can estimate doubling time without a calculator. Divide 72 by the annual rate in percent, and the result is roughly how many years it takes money to double. At 8% that is about nine years; at 4% it is about 18.
Run it backward and the rule shows how damaging high rates are for borrowers. A credit card charging 24% doubles an unpaid balance in about three years. It also works for inflation: at 6% inflation, prices double in about 12 years, halving what your cash can buy.
Compound Interest vs. Simple Interest
| Compound Interest | Simple Interest | |
|---|---|---|
| Interest calculated on | Principal plus accumulated interest | Principal only |
| Growth pattern | Accelerating (exponential) | Constant (linear) |
| $10,000 at 7% for 30 years | About $76,100 | $31,000 |
| Common uses | Savings accounts, credit cards, reinvested returns | Many car loans, some short-term notes |
Why Is Compound Interest Important for Traders?
Compounding is why reinvesting matters. An investor who reinvests every dividend buys more shares, which pay more dividends, which buy more shares. The same logic drives crypto staking and auto-compounding vaults, where rewards are restaked so that the next payout is calculated on a larger balance.
But the math that builds wealth also magnifies losses. Returns compound multiplicatively, so a 50% loss followed by a 50% gain leaves $100 at $75, not back at $100. The more volatile an asset, the wider the gap between its average annual return and what you actually earn, which is why large drawdowns hurt long-term results more than they seem to at first glance.
Costs compound too, and that is where compounding turns against traders. A 2% annual fee on a portfolio earning 7% cuts the 30-year result from about $76,000 to about $43,000 on a $10,000 start. Overnight financing on leveraged positions and interest on margin trading loans work the same way, eating a growing share of returns the longer a position stays open.
Key Takeaways
- Compound interest is calculated on both the principal and the interest already earned, so growth accelerates with every period.
- Time is the most powerful input in the formula: the final decade of a 30-year compounding period often adds more than the first two decades combined.
- The Rule of 72 gives a quick estimate of doubling time by dividing 72 by the annual rate in percent.
- More frequent compounding raises the effective annual yield, which is why the same headline rate can produce different results.
- Compounding applies equally to losses, debt, inflation and fees, so it can erode wealth as reliably as it builds it.
How often is interest compounded?
It depends on the product. Savings accounts often compound daily or monthly, many bonds pay semi-annually, and credit cards usually compound daily, which is why card debt grows faster than its headline rate suggests.
Does compound interest apply to stocks?
Stocks do not pay interest, but reinvested dividends and retained profits compound in the same way. The growth is not guaranteed, because returns vary from year to year and can be negative.
What is the Rule of 72?
The Rule of 72 estimates how many years money takes to double by dividing 72 by the annual rate. At 6% it takes about 12 years, and the shortcut is most accurate for rates between roughly 5% and 10%.
Can compounding make losses worse?
Yes. Losses compound too, so a 50% drop needs a 100% gain just to break even, and borrowed money at a compound rate can outgrow your ability to repay it.
