Why compound interest grows faster than it seems

Simple interest pays you the same amount every period, based only on your original balance. Compound interest pays you interest on your interest — each period's earnings get added to the balance, and the next period's interest is calculated on that larger number. Over short periods the difference looks small; over years or decades it becomes the entire reason long-term investing works the way it does. Albert Einstein is often (probably apocryphally) credited with calling compound interest one of the most powerful forces in finance, and the underlying math backs up the sentiment even if the quote itself is disputed.

The formula, with monthly contributions

This calculator compounds monthly and adds your monthly contribution at the end of each month, which is how most real savings accounts and retirement contributions actually work:

Balance after each month = (previous balance + contribution) × (1 + monthly rate)

What matters most: rate, time, or contribution size?

Time tends to matter more than most people expect — a smaller amount invested for twice as long can end up ahead of a larger amount invested for half the time, purely because compounding needs time to do its work. That's the core argument for starting early even with small amounts, rather than waiting to have a "meaningful" sum to invest. This calculator assumes a constant rate of return for simplicity — real markets fluctuate year to year, so treat the result as a rough long-term estimate, not a guarantee.