Your contributions stack in blue, the interest they earn stacks in green — and the line shows the whole pile deflated to today's purchasing power. Watch interest overtake contributions.
The pattern to notice: in the early years your deposits do the heavy lifting; in the late years the interest does. At 7%, the last decade of a 30-year run typically earns more than the first two combined — which is exactly why the next tab's question, "what does waiting cost?", has such an uncomfortable answer.
Start with what you have, add what you can each month, and let the compounding do the rest. Interest earns interest — that's the whole trick.
Projected balance under the solved plan, against the goal line.
Reading the answer: when interest covers most of the target, time is doing the work and the plan is robust. When your contributions cover most of it, the timeline is short enough that the return barely matters — a savings account and an index fund land in nearly the same place over three years, and nowhere near the same place over thirty.
Pick the target and what you know; this solves for the missing piece — the monthly contribution, the time it takes, or the return you'd need.
The gap between the curves never closes — it widens. The delayed saver isn't a few years behind at the end; they're missing the years that would have earned the most.
Why the gap is so lopsided: the deposits you skip by waiting are the ones with the most years left to grow. Skip five $6,000 years at the start of a 30-year run at 7% and each of those dollars forfeits roughly five doublings' worth of tail growth — which is how a $30,000 pause becomes a six-figure hole.
Two savers, identical in every way, except one starts today and one starts after a delay. Same monthly amount, same return, same finish line.
Years to double across return rates. The rule shadows the truth remarkably well through the middle rates — it's calibrated around 8% — and drifts at the extremes.
Where 72 comes from: the exact doubling time is ln 2 ÷ ln(1 + r) ≈ 69.3/r for small rates. The number 72 won the mental-math contest because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12 — and conveniently, the approximation it produces is nearly perfect right around typical investment returns.
The Rule of 72 — divide 72 by the return — is the oldest mental shortcut in finance. Here it sits next to the exact answer so you can see how good it really is.
A sustainable plan drifts up or holds flat; an unsustainable one arcs over and dives. The shape tells you which side of the line you're on well before the ending does.
About the famous 4% rule: withdrawing 4% of the starting balance, inflation-adjusted, historically survived every 30-year US retirement — that's where the benchmark comes from. This model uses one steady return; real markets deliver the average unevenly, and bad years early in retirement hurt far more than the same years late. Treat the answer as a compass bearing, not a guarantee.
The reverse question: you've built the pile — now you're spending it while what remains keeps growing. How long does it hold out?