The real magic,
measured.
The annual rate is treated as an effective annual return: on a lump sum, the horizon-end value equals initial × (1 + r)years. Monthly contributions are added at the end of each month. Not investment advice — a thinking tool.
“Little by little steps creates wonders. Do not interrupt it unnecessarily.”— Third law of reasonable investment decisions
Compound interest, as it actually behaves.
The calculator projects the value of an initial capital plus a fixed monthly contribution, compounded at a rate you set, over a horizon you choose. The stacked chart separates what you actually put in from what the market gives back to you — because that split, more than the final number, is what tells you whether the plan works.
The percentage you type is the effective annual return: a lump sum grows by exactly that much in one year. Internally, monthly compounding uses r_month = (1 + r_annual)^(1/12) − 1, so lump-sum growth matches (1 + r)^years exactly. This is different from the APR convention (r/12) that overstates results — a subtle 0.2 to 0.4 percentage-point error over long horizons.
Contributions form the grey base of the chart; interest is the green wedge that widens with time. Early on, interest is a rounding error. Somewhere between years ten and fifteen it usually overtakes contributions — that crossover is the whole point of the exercise. Slide the horizon back and forth and watch where it lands: if the plan needs it earlier than that, you probably need either more monthly savings or a more realistic return assumption.