The compound interest formula
For a single deposit, the future value is:
where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. Regular contributions are added as a series of monthly deposits (an annuity), each growing for the time remaining:
Here C is the monthly contribution, m the number of months and i the monthly growth rate equivalent to your compounding choice. Contributions are assumed at the end of each month.
Why time matters more than anything else
In the example above, the balance after 10 years is about $54,700. The second decade adds almost $90,000 because interest is now being earned on a much larger base. Starting early — even with small amounts — usually beats contributing more later.
Where compound interest applies
- High-yield savings accounts and CDs — usually compounded daily or monthly.
- Bonds and bond funds — interest reinvested compounds over time.
- Stock index funds — returns are not guaranteed, but reinvested dividends and growth compound in a similar way. Using a long-run average return (for example 6–8% before inflation) gives a rough projection.
- Debt — credit cards compound against you. See the credit card payoff calculator.
How to use the calculator
- Enter your starting amount (principal).
- Enter how much you will add each month, if anything.
- Enter the expected annual interest rate or return and how often it compounds.
- Enter the number of years and read the final balance, total contributions and interest earned, with a year-by-year breakdown.
Growth over time
$10,000 to start, $200 a month, 7% compounded monthly:
| Years | Total deposited | Interest earned | Balance |
|---|---|---|---|
| 5 | $22,000 | $6,495 | $28,495 |
| 10 | $34,000 | $20,714 | $54,714 |
| 20 | $58,000 | $86,573 | $144,573 |
| 30 | $82,000 | $243,159 | $325,159 |
| 40 | $106,000 | $582,077 | $688,077 |
In the first decade, most of the balance is your own deposits. After about 20 years, interest earned overtakes what you put in, and by 40 years it is several times larger.
Starting early vs. saving more
Choosing a realistic rate
- High-yield savings and CDs: close to short-term interest rates, which change over time.
- Bonds: historically a few percent a year.
- Diversified stock index funds: U.S. stocks have returned about 10% a year on average over the long run before inflation, or roughly 6–7% after inflation, with large ups and downs along the way.
To see results in today’s money, use an after-inflation (real) rate, or adjust the final balance with the inflation calculator. Investment returns are never guaranteed, and past performance doesn’t predict future results.
What reduces compounding
- Fees: a 1% annual fee takes a large share of growth over decades. Low-cost index funds often charge under 0.1%.
- Taxes: tax-advantaged accounts such as 401(k)s and IRAs let returns compound without yearly taxes.
- Withdrawals and missed contributions: stopping contributions for a few years early on costs more than it seems, because those dollars miss decades of growth.