Monte Carlo Retirement Calculator (Success Rate & Ending Balance Range)

How it works

each year: balance = (balance − withdrawal) × e^(g + σₗ·Z), Z ~ N(0,1), σₗ² = ln(1 + σ² ÷ (1 + μ)²), g = ln(1 + μ) − σₗ²/2, so the growth factor has mean 1 + μ and standard deviation σ withdrawal = first-year amount × (1 + inflation)^(year − 1) − other income (fixed rule); guardrails cut or raise it 10% when the withdrawal rate drifts 20% from its start; percentage rule = rate × balance success = paths that never run out ÷ 2,000 · percentiles from the sorted balances · seeded random numbers, so the same inputs always give the same result

A straight-line projection at the average return hides what actually breaks retirements: the order in which good and bad years arrive while you are withdrawing. A Monte Carlo simulation draws 2,000 plausible sequences of yearly returns from your expected return and volatility, runs your plan through each one, and reports how often the money lasts and how wide the range of outcomes is. A plan that works on average can still fail one time in five. The chart shows percentile bands: in any year, a tenth of the paths are below the 10th-percentile line and half are below the median. You can choose how withdrawals behave. A fixed amount raised with inflation is the classic 4% rule. Guardrails cut spending 10% when the withdrawal rate drifts well above where it started and raise it after strong markets. A percentage rule takes the same share of whatever is left each year. Flexible rules fail less often but your income moves with the markets, so the calculator also shows the lowest spending they lead to. Other income such as a pension or Social Security reduces what the portfolio must provide, and you can simulate the years you are still saving. The solver finds the highest first-year spending that still reaches your target success rate on the same paths. The success rate is a planning gauge rather than a prediction. It is most sensitive to the withdrawal rate, the assumed return and the early years. Random numbers come from a fixed seed, so the same inputs always give the same answer; change the seed to see the sampling noise.

Worked example

A $1,000,000 portfolio paying $40,000 a year (4%), rising with 2.5% inflation, at a 7.3% net return with 11% volatility over 30 years, lasts in about 88% of 2,000 simulated paths. The median path ends near $2.0 million in future dollars, about $960,000 in today’s money, while the 10th percentile ends at zero and the 90th above $6 million. A steady 7.3% return would never run out, which is the sequence-risk gap. Cutting to $35,000 (3.5%) lifts success to about 95%, and the highest first-year spending with 90% success is about $38,300. Switching to guardrails at the same $40,000 means the money almost never runs out, but on one path in ten spending falls below about $18,300 in today’s money at some point.

Frequently asked questions