Enter your investment details to see how your money grows.
How Compound Interest Works
$10,000 invested at 7% compounded monthly grows to $20,097 in 10 years and $81,165 in 30 years, without adding another dollar. Compound interest pays interest on the interest you already earned, so growth speeds up the longer the money stays invested. Enter a starting amount, rate, time and an optional monthly deposit above to see your future value, total interest and doubling time.
Compound interest means you earn interest not just on your principal, but also on the interest you've already earned. Einstein allegedly called it "the eighth wonder of the world", and the math backs that up.
The formula: A = P(1 + r/n)^(nt) where P = principal, r = annual rate, n = compounds per year, t = years. With monthly contributions, each payment compounds for the remaining time.
A simple example: $10,000 at 7% annually for 30 years grows to $76,123 with no contributions. Add $200/month and it becomes $311,336, over $220,000 in interest earned on just $82,000 invested.
The Compound Interest Formula, Step by Step
For a single deposit the formula is A = P(1 + r/n)nt. Take $10,000 at 7% compounded monthly for 10 years:
- Rate per period: 0.07 ÷ 12 = 0.005833.
- Number of periods: 12 × 10 = 120.
- Growth factor: 1.005833120 = 2.00966.
- Future value: $10,000 × 2.00966 = $20,097, of which $10,097 is interest.
Adding monthly deposits
Regular deposits are a series of small investments, each compounding for the time it has left. This calculator treats deposits as made at the start of each month, using FV = D × ((1 + i)N − 1) ÷ i × (1 + i), where i is the monthly rate and N the number of months. $200 a month at 7% for 10 years grows to $34,819 from $24,000 deposited. Add the $10,000 starting balance and you get $54,916, which is exactly what the calculator shows with its default inputs.
When interest compounds annually, quarterly or daily but you deposit monthly, the calculator converts the rate to its monthly equivalent, (1 + r/n)n/12 − 1, so each deposit earns the right amount for the time it is invested.
Compound Growth Tables
$10,000 invested once, compounded monthly
| Annual rate | 10 years | 20 years | 30 years | 40 years |
|---|---|---|---|---|
| 4% | $14,908 | $22,226 | $33,135 | $49,399 |
| 5% | $16,470 | $27,126 | $44,677 | $73,584 |
| 6% | $18,194 | $33,102 | $60,226 | $109,575 |
| 7% | $20,097 | $40,387 | $81,165 | $163,114 |
| 8% | $22,196 | $49,268 | $109,357 | $242,734 |
| 10% | $27,070 | $73,281 | $198,374 | $537,007 |
$500 deposited every month, starting from zero
| Annual rate | 10 years | 20 years | 30 years | 40 years |
|---|---|---|---|---|
| You deposit | $60,000 | $120,000 | $180,000 | $240,000 |
| 4% | $73,870 | $183,999 | $348,181 | $592,951 |
| 5% | $77,965 | $206,373 | $417,863 | $766,189 |
| 6% | $82,349 | $232,176 | $504,769 | $1,000,724 |
| 7% | $87,047 | $261,983 | $613,544 | $1,320,062 |
| 8% | $92,083 | $296,474 | $750,148 | $1,757,141 |
| 10% | $103,276 | $382,848 | $1,139,663 | $3,188,390 |
Look at the 7% row: in the first 10 years interest adds $27,047 to your deposits, while in the last 10 years alone the balance grows by more than $700,000. That late surge is compounding at work, and it only happens if the money is left alone.
Compounding Frequency and the Rule of 72
More frequent compounding helps, but far less than a higher rate or a longer time. APY (annual percentage yield) shows the real yearly return after compounding, which is why banks quote it.
| Compounding | APY on a 5% rate | $10,000 at 7% after 10 years |
|---|---|---|
| Annually | 5.000% | $19,672 |
| Quarterly | 5.095% | $20,016 |
| Monthly | 5.116% | $20,097 |
| Daily | 5.127% | $20,136 |
The Rule of 72 estimates doubling time as 72 divided by the rate. Here is how close it gets to the exact answer with annual compounding:
| Rate | Rule of 72 | Exact years to double |
|---|---|---|
| 3% | 24.0 | 23.4 |
| 4% | 18.0 | 17.7 |
| 5% | 14.4 | 14.2 |
| 6% | 12.0 | 11.9 |
| 7% | 10.3 | 10.2 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
Why Starting Early Wins
Two savers earn 7% a year, compounded monthly. Saver A puts in $200 a month from age 25 to 35, then stops: $24,000 in total. Saver B waits, then puts in $200 a month from 35 to 65: $72,000 in total. At 65, Saver A has $282,607 and Saver B has $245,417. The ten extra years of compounding beat three times the deposits.
Common mistakes with compound interest
- Ignoring inflation. A 7% return with 3% inflation grows buying power by only about 3.9% a year. Use a real rate if you want the answer in today's dollars, or check our inflation calculator.
- Forgetting fees and taxes. A 1% yearly fee turns a 7% return into 6%, and over 30 years that cuts the value of a $10,000 deposit from $76,123 to $57,435 (annual compounding). Interest in a taxable account is taxed every year, which slows compounding.
- Confusing APR with APY. Compare savings accounts by APY and loans by APR, and remember that credit card debt compounds against you the same way savings compound for you.
- Treating a stock return like a fixed rate. Stocks do not earn a steady 7%; they move around it. The tables show the average path, not a guarantee.
For a plan with a target date, try the savings goal calculator or the retirement calculator.