Compound interest is interest earned on interest. That one idea explains why small savings habits grow into large balances, why starting early matters so much, and why credit card debt can spiral. It also works against you through fees and inflation, which is the half of the story most explanations skip.
This guide covers the formula, the effect of compounding frequency, the rule of 72 for quick mental math, and a few worked examples you can check yourself in the compound interest calculator.
Simple interest vs compound interest
With simple interest, you earn interest only on your original deposit. With compound interest, each period’s interest is added to the balance, so next period you earn interest on a slightly bigger number.
Take $10,000 earning 6% a year. With simple interest you earn $600 every year, forever. With annual compounding you earn $600 in year one, $636 in year two and $674 in year three, and by year 30 that year’s interest alone is $3,251.
| After | Simple interest | Compound interest (annual) |
|---|---|---|
| 1 year | $10,600 | $10,600 |
| 10 years | $16,000 | $17,908 |
| 20 years | $22,000 | $32,071 |
| 30 years | $28,000 | $57,435 |
For the first few years the two lines are almost identical. After that they separate quickly. That slow start is why compounding feels underwhelming at first and powerful later. If you want to see the simple version on its own, the simple interest calculator shows both side by side.
The compound interest formula
A = P × (1 + r ÷ n)^(n × t)A is the final amount, P the starting balance, r the annual interest rate as a decimal, n the number of compounding periods per year and t the number of years.
For $10,000 at 6% compounded once a year for 30 years: A = 10,000 × 1.06^30 = $57,434.91.
Most people also add money regularly. The future value of a series of equal deposits made at the end of each period is:
FV = PMT × ((1 + i)^N − 1) ÷ iPMT is the regular deposit, i the interest rate per period (for monthly deposits, the annual rate ÷ 12) and N the total number of deposits.
You rarely need to do this by hand, but knowing the shape of the formula helps. Time sits in the exponent, which is why years matter more than almost anything else.
How compounding frequency changes the result
Interest can be added yearly, quarterly, monthly or daily. The more often it is added, the sooner your interest starts earning interest. The true annual rate you end up with is called the effective annual rate (EAR). On US savings accounts it is disclosed as the annual percentage yield (APY), and in the UK as the annual equivalent rate (AER).
EAR = (1 + r ÷ n)^n − 1r is the quoted (nominal) annual rate and n the compounding periods per year.
Here is a 6% quoted rate at different frequencies, applied to $10,000 for 30 years:
| Compounding | Effective annual rate | Value after 30 years |
|---|---|---|
| Annually | 6.000% | $57,435 |
| Semi-annually | 6.090% | $58,916 |
| Quarterly | 6.136% | $59,693 |
| Monthly | 6.168% | $60,226 |
| Daily | 6.183% | $60,488 |
Frequency matters, but less than people expect. Moving from annual to daily compounding adds about 0.18 percentage points a year. Moving from a 6% account to a 6.5% account would do far more. The practical rule is simple: compare savings accounts by APY or AER, which already include compounding, rather than by the headline rate.
Loans work the other way round. In the US, the APR on a loan does not include the effect of compounding, so a card with a 24% APR charged monthly actually costs about 26.8% a year. Our guide to APR vs interest rate explains what each figure does and doesn’t include. Conventions differ by country too: Canadian fixed-rate mortgages, for example, are typically compounded semi-annually rather than monthly.
The rule of 72
The rule of 72 is a shortcut for estimating how long it takes money to double:
Years to double ≈ 72 ÷ annual interest rate (in %)Use the rate as a whole number: for 6%, divide 72 by 6.
At 6%, 72 ÷ 6 = 12 years. The exact answer is 11.9 years, and $10,000 at 6% for 12 years grows to $20,122, so the shortcut is very close.
You can run it backwards too. If you want to double your money in 10 years, you need roughly 72 ÷ 10 = 7.2% a year. The exact figure is 7.18%.
And you can chain it. Two doublings means four times your money, so at 6% you would expect $10,000 to reach about $40,000 in roughly 24 years. The exact figure after 24 years is $40,489.
Quick check: the rule of 72 is a sanity test, not a planning tool. Use it to spot a claim that sounds too good, such as an investment "doubling in three years", which implies about 24% a year. Then do the real math.
Rule of 69, 70 or 72: which is best?
The exact doubling time is ln(2) ÷ ln(1 + r). For small rates this is close to 0.693 ÷ r, which is where 69.3 comes from. So why do most people use 72?
- 72 is easy to divide by 2, 3, 4, 6, 8, 9 and 12, and it happens to be most accurate around 8%, a common range for long-term return assumptions.
- 70 is a little more accurate at low rates, so economists often use it for inflation or growth rates of 1% to 3%.
- 69.3 (sometimes rounded to 69) is exact for continuous compounding, the theoretical limit of compounding more and more often.
| Rate | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact (annual compounding) |
|---|---|---|---|---|
| 2% | 36.0 | 35.0 | 34.7 | 35.0 |
| 4% | 18.0 | 17.5 | 17.3 | 17.7 |
| 6% | 12.0 | 11.7 | 11.6 | 11.9 |
| 8% | 9.0 | 8.8 | 8.7 | 9.0 |
| 10% | 7.2 | 7.0 | 6.9 | 7.3 |
| 12% | 6.0 | 5.8 | 5.8 | 6.1 |
| 20% | 3.6 | 3.5 | 3.5 | 3.8 |
For everyday use, any of them is close enough. At very high rates, all three start to underestimate the time.
Starting early vs starting late
Because time sits in the exponent, the years you invest matter more than the amount you put in. Consider two savers who each invest $200 a month and earn an assumed 7% a year, compounded monthly.
Worked example: Alex and Sam
Alex invests $200 a month from age 25 to 35, then stops and never adds another dollar. Total contributed: $24,000. Balance at 35: $34,617. Balance at 65: $280,968.
Sam waits until 35, then invests $200 a month for 30 years until 65. Total contributed: $72,000. Balance at 65: $243,994.
Alex put in a third as much and still finished ahead. To match Alex, Sam would need to invest about $230 a month for all 30 years.
Someone who did both, $200 a month from 25 all the way to 65, would contribute $96,000 and end with $524,963.
Real returns are never a smooth 7% a year, and nothing here is a forecast. But the pattern holds at any steady rate: money invested earlier has more doublings ahead of it. If you are planning for a specific target, the retirement calculator and the savings goal calculator let you work backwards from the number you need.
Fees: compounding in reverse
An annual fee is taken from your balance every year, so it compounds just like returns do, only against you. A fee that looks small on a statement can claim a large share of your final balance.
Here is $100,000 left to grow for 30 years at an assumed 7% return before fees:
| Annual fee | Net return | Value after 30 years | Lost to fees |
|---|---|---|---|
| 0% | 7.0% | $761,226 | None |
| 0.5% | 6.5% | $661,437 | $99,789 |
| 1.0% | 6.0% | $574,349 | $186,876 |
| 2.0% | 5.0% | $432,194 | $329,031 |
A 1% fee costs about a quarter of the final balance. That is why fund fees, platform fees and advice fees deserve as much attention as returns. You can’t control the market, but you can usually control what you pay.
Inflation and debt: compounding against you
Inflation compounds too. At 3% inflation, the rule of 72 says prices double in about 24 years, so a dollar buys half as much. Precisely, $100 today would have the buying power of $49.19 after 24 years.
To see what an investment really earns, look at its real return: (1 + nominal return) ÷ (1 + inflation) − 1. A 7% return with 3% inflation is a real return of about 3.9%, not 4%. The $57,435 from the first example, earned over 30 years with 3% inflation, buys what $23,662 buys today.
Cash is not safe from this either. A savings account paying 2% while inflation runs at 3% loses about 1% of its buying power every year: after 10 years, $10,000 would buy what about $9,070 buys today. The inflation calculator shows this for any rate.
Debt is the other place compounding hurts. At a 24% APR compounded monthly, an unpaid $1,000 card balance doubles to about $2,040 in three years, just as the rule of 72 predicts (72 ÷ 24 = 3). That is why paying off high-interest debt is often the best guaranteed return available. Our credit card payoff calculator shows how long a balance takes to clear, and the guide to the debt snowball vs avalanche helps you choose an order of attack.
Mortgages compound as well, which is why extra repayments early in a loan save so much interest. See how mortgage amortization works and how to pay off your mortgage faster for the details.
The short version
- Compounding rewards time above everything else, so start as early as you can, even with small amounts.
- Compare savings by APY or AER, not the headline rate, and compare loans by their total cost.
- Use the rule of 72 to sanity-check claims and to feel the difference between rates.
- Treat fees, inflation and high-interest debt as compounding in reverse, and cut them where you can.
This guide is general information, not personal financial advice. Rules and products vary by country and lender.