How compound interest builds wealth over time
Compound interest is often called the eighth wonder of finance, and the reason is simple: you earn interest not just on the money you put in, but on every dollar of interest that money has already earned. Each compounding period your balance is a little larger, so the next round of interest is calculated on a bigger base. Repeat that for years or decades and growth that starts out gentle curves sharply upward — the longer your time horizon, the more dramatic the effect.
The formula this calculator uses
The future value of your starting amount uses the standard compound interest equation
FV = P × (1 + r/n)^(n×t), where P is the principal,
r is the annual rate as a decimal, n is how many times a year
interest compounds, and t is the number of years.
Regular monthly contributions are added as an ordinary annuity. With a monthly
rate i = r/12 over N = 12×t months, their combined future value is
PMT × ((1 + i)^N − 1) / i. If the rate is zero this reduces to simply
PMT × N. The final balance is the grown principal plus the grown contributions;
total interest is the final balance minus everything you actually put in.
A worked example
Start with $10,000 at 7% compounded monthly for
20 years, adding $200 every month. The principal alone grows to
10,000 × (1 + 0.07/12)^240 ≈ $40,387. The 240 monthly $200 deposits grow to
about $104,185, for a final balance near $144,573. Of that, you
personally contributed $58,000 ($10,000 plus 240 × $200) — the remaining
$86,573 is pure compound interest. The exact figures appear above as you type.
Why frequency matters less than time
The same $10,000 at 7% for 20 years, with no contributions, by compounding frequency:
| Compounding | Final balance | vs. annual |
|---|---|---|
| Annually | $38,697 | — |
| Quarterly | $40,064 | +$1,367 |
| Monthly | $40,387 | +$1,691 |
| Daily | $40,547 | +$1,850 |
Moving from annual to daily compounding adds only a few percent over two decades. Adding years, raising the rate, or contributing regularly each move the needle far more — which is why starting early and staying consistent beats chasing the perfect account.