The single most important math in personal finance, finally shown instead of just described. Move the sliders. Watch the curve. Notice how the steepness in the last decade dwarfs the first four. That's compounding doing its job — and that's why every year you wait costs more than the last.
Two formulas:
FVlump = P × (1+r)n — your starting amount, compounded monthly over n months at monthly rate r = annual ÷ 12.
FVannuity = C × ((1+r)n − 1) / r — your monthly contributions, also compounded monthly. The two are added together for the final balance.
The default 7% return is the rough long-run S&P 500 real (post-inflation) return. Nominal is closer to 10%, but real-return numbers are what you actually live on. The curve here assumes you stay invested through every downturn — which is the part the math doesn't show but the historical record demands.
Most of the final balance comes from growth, not from contributions. In the default setup ($1k + $200/mo for 30 years at 7%), you contribute $73,000 and end with ~$245,000 — meaning ~70% of what you have at year 30 was earned, not deposited. That's compounding doing the work, not your salary.
The same math also means starting late is brutally expensive. Drop the horizon from 40 years to 30 years and the final balance roughly halves, even though you only "skipped" 10 years of contributions worth ~$24,000. Time is the single most powerful input — more than the return rate, more than the monthly amount.
This is also why we built the subscription cost calculator as a companion: every recurring dollar spent is a recurring dollar that doesn't compound. Use both. The lens is the math.