Saving & Investing
How Compound Interest Works (With a Free Calculator)
Educational content, not personalized financial advice. Read the disclaimer.
Compound interest means you earn interest on your interest. In the first few years the effect is small. Over decades it can become the largest part of a balance. Here is the formula, a worked example, and what the numbers can and can't tell you.
The idea in one sentence
Simple interest is paid only on the amount you started with. Compound interest is paid on the starting amount plus the interest already added. Here is $1,000 growing at 5% a year:
| After | Simple interest | Compound interest (yearly) |
|---|---|---|
| 10 years | $1,500.00 | $1,628.89 |
| 20 years | $2,000.00 | $2,653.30 |
| 30 years | $2,500.00 | $4,321.94 |
The gap widens over time because each year's interest becomes part of next year's starting amount.
The formula
A = P × (1 + r ÷ n)n × t- A is the final amount.
- P is the starting amount (the principal).
- r is the annual rate as a decimal (5% is 0.05).
- n is how many times per year interest is added.
- t is the number of years.
Example: $1,000 at 5%, added once a year, for 10 years: 1,000 × 1.0510 = $1,628.89.
Adding regular contributions
Most people don't invest one lump sum. They add money every month. For equal deposits at the end of each month, the balance is:
FV = P × (1 + i)N + PMT × [ ((1 + i)N − 1) ÷ i ]Here i is the monthly rate (the annual rate divided by 12), N is the number of months and PMT is the monthly deposit. Try it with the calculator below.
Say you start with nothing and add $200 a month at a hypothetical 6% a year, compounded monthly:
| Years | You put in | Growth | Balance |
|---|---|---|---|
| 20 | $48,000 | $44,408 | $92,408 |
| 30 | $72,000 | $128,903 | $200,903 |
Thirty years is only 50% more time than twenty, but the balance is more than double. In the longer scenario, growth is larger than everything you deposited. That is why people say time matters more than almost anything else in compounding.
The Rule of 72
A quick way to estimate how long money takes to double: divide 72 by the annual rate. At 6%, 72 ÷ 6 = 12 years. The exact answer is about 11.9 years, so the shortcut is close. It is only an approximation, but it is handy for mental math.
What the calculator can't tell you
- Real returns are not steady. The calculator assumes the same rate every year. Actual investment returns change from year to year and can be negative, and nothing guarantees any particular rate. Savings accounts pay rates that also change over time.
- Inflation. A larger number in the future buys less than the same number today. See what inflation does to your savings.
- Taxes and fees. Both reduce what you keep, and fees compound against you just as growth compounds for you.
- The same math works against borrowers. Interest on debt compounds too, which is why balances can be hard to pay down. See debt snowball vs. avalanche.
Putting it to use
- Start early, even with a small amount. Time is the one input you can't buy later.
- Automate contributions. Regular deposits are the second engine in the formula.
- Pay attention to costs. Compare fees and rates using the same measure, such as APY. See APR vs. APY.
- Build a safety cushion first so you never have to pull money out at a bad time. See how much to keep in an emergency fund.
This is educational content, not investment advice. The examples use hypothetical numbers. For free investor education from the SEC's Office of Investor Education and Advocacy, visit Investor.gov.