The calculator
Drawing $40,000 a year from $1,000,000 for 30 years, at a 7.0% mean return with 15.0% volatility, survived in 766 of 1000 paths (seed 20260828). The middle path ended at $1,379,838; the worst tenth ended at or below $0. The constant 7.0% line ended at $2,646,690.
| Year | 10th percentile | Median | 90th percentile | Constant-return line |
|---|---|---|---|---|
| 10 | $513,680 | $1,176,576 | $2,292,610 | $1,326,729 |
| 20 | $112,271 | $1,359,809 | $4,139,447 | $1,829,206 |
| 30 | $0 | $1,379,838 | $7,014,120 | $2,646,690 |
Versus a single 7% line
A spreadsheet that compounds 7.0% every year on these inputs ends at $2,646,690 and never runs out. That is not a forecast. It is one sequence: the sequence in which every year is the mean. The 1,000-path band is 1,000 other sequences. 234 of them emptied the portfolio before year 30. The 10th percentile ended at $0. Those two facts have nowhere to print on a single line, which is why this page exists.
Set volatility to 0% and the band collapses onto that line. That is the honest check that the engine is doing arithmetic, not theatre.
How the success rate is computed
There is no formula behind a success rate, only arithmetic repeated a thousand times. Each path draws a return for every year from a lognormal distribution with the mean and volatility above, takes the withdrawal at the start of each year, indexes that withdrawal to inflation, and records whether the money lasted the horizon. The success rate is the count that lasted divided by the count that ran: 766 ÷ 1000 = 77% with the inputs above.
That also tells you how much precision the number carries. A success rate is a binomial proportion, so at 1,000 paths an 85% result sits within roughly two points either side, and at 100 paths it is nearer seven. Quoting a success rate to one decimal place implies a precision the sample size does not support, which is why this page rounds. The arithmetic is in how many Monte Carlo simulations is enough.
The 1,000-lifetime study
This calculator is independent lognormal draws. The published Monte Carlo retirement planning study uses the five-regime engine on the same $1,000,000 / $40,000 / 30-year case, seed 20260622: 89.6% success, 10.4% ruin, real p10 $0, p50 $1,083,603, p90 $5,692,838, against a 7% deterministic ending of $1,727,805. Different engines, different clustering of bad years, different success rates. Compare plans inside one engine. Download that study CSV. The button above exports this page's lognormal run, not that freeze.
Related calculators
A first-year cheque from a rate is the safe withdrawal rate calculator. The locked 4% identity is the 4% rule calculator. Order of returns, holding the average fixed, is the sequence of returns risk calculator. Spending rules that flex are the Guyton-Klinger calculator and the Vanguard dynamic spending calculator. The accumulation counterpart is the Coast FIRE calculator. A university-style blend of last year's spend and a target rate is the Yale spending rule.
Versus the live demo
This band is independent lognormal draws around the mean you typed. The live household demo uses Killion’s five-regime engine, an allocation, and a crash you can place. The methodology page is the product model. How to read a Monte Carlo is the explainer. How many Monte Carlo simulations is enough is why this page uses 1,000 paths.
Assumptions
1,000 paths, seed 20260828, start-of-year withdrawals, returns drawn independently each year, no fees and no taxes. Independent draws are the simplification that matters most: real markets cluster bad years together, which is what the five-regime engine behind the methodology reproduces and this page does not. A fixed seed means the same inputs give the same answer, so a figure you quote today reproduces tomorrow. Not a forecast.