How compound interest is calculated
Compound interest is interest earned on interest. Each time interest is added to your balance, the next round of interest is calculated on the bigger amount, so growth speeds up over time. With regular contributions on top, the effect is even stronger. In the chart above, the gap between your contributions and the total balance is the interest, and it widens every year.
The formula
For a single deposit, the future value is:
A = P × (1 + r/n)^(n × t)- P is the starting amount.
- r is the annual interest rate as a decimal (7% is 0.07).
- n is the number of times interest compounds per year (12 for monthly).
- t is the number of years.
For a monthly contribution PMT made at the end of each month with monthly compounding, the contributions grow to PMT × ((1 + r/12)^(12t) − 1) / (r/12). The total is the sum of the two parts.
When the compounding frequency is not monthly, this calculator converts the rate to its monthly equivalent, (1 + r/n)^(n/12) − 1, and adds deposits at the end of each month. That keeps the starting amount growing exactly as the formula above while treating monthly deposits fairly.
A worked example
$10,000 invested at 7% compounded monthly, with $500 added each month for 20 years: the starting amount grows to about $40,387 and the contributions to about $260,463, for a total near $300,850. You put in $130,000, so more than half of the final balance is interest.
What makes the biggest difference
- Time. Because growth is exponential, the last few years add far more than the first few. Drag the years slider and watch the interest band grow.
- Rate. A difference of one or two percentage points adds up to a large gap over decades.
- Compounding frequency matters much less than people expect. At 7%, monthly compounding gives an effective annual rate of 7.23% and daily compounding 7.25%.
The rule of 72
To estimate how long it takes money to double, divide 72 by the annual rate. At 6% it takes about 12 years, at 9% about 8 years. This works for rates between roughly 4% and 12%.
These figures ignore taxes, fees and inflation, and real investment returns vary from year to year. Treat the result as an estimate, not a promise.
