The Model Behind These Results
Each year draws a nominal simple return r = mean + volatility × Z, where Z is a standard normal random draw independent of other years. The gross return is floored at zero, so a modeled investment loss cannot exceed 100%. This is an annual normal-return model, not geometric Brownian motion, a historical bootstrap or a multi-asset allocation model.
For a path that has not depleted, the next balance in today’s dollars is: previous balance × max(0, 1 + r) / (1 + inflation) + annual contribution − annual withdrawal. Cash flows occur at year-end and stay constant in real terms. If the resulting balance is zero or negative, that path is set to zero permanently.
Build and Compare Scenarios
- Enter starting capital above zero and nonnegative yearly contributions and withdrawals in today’s dollars. Cash flows cannot change by age or year in this tool.
- Choose 1–60 whole years and a constant inflation assumption. A longer withdrawal period can expose additional depletion risk; it is not a remedy for low survival.
- Enter nominal arithmetic mean return and annual standard deviation. The example presets are illustrative numbers without a historical sample or asset allocation calculation.
- Run a scenario, note the inputs and download the CSV. Change one assumption at a time and compare the survival frequency and lower-tail values.
- Test adverse assumptions as well as your central case. The model excludes taxes, fees, asset correlations, regime changes, variable inflation and intra-year cash-flow shortfalls.
Percentiles, Survival and Sampling Error
Survival is the share of paths positive at every simulated year-end. The median and percentile columns summarize separate yearly distributions; joining these values would not produce one investor’s actual path. The implementation selects sorted observations at floor(p × sample count), with p written as a decimal. A 10th percentile value is not a worst-case floor.
The screen displays the start, every fifth year and the final year. CSV includes every year’s median, 10th and 90th percentiles and survival rate. Fresh random draws mean repeated runs can differ. More draws reduce sampling noise within this model but cannot validate its assumptions.
Use the Output as a Sensitivity Exercise
Normal independent returns do not reproduce all market tails or persistent stress periods. Capping losses also changes the distribution when extreme returns are sampled. No survival percentage is labeled safe, and this tool does not recommend a withdrawal rate or portfolio.
The simulation runs in this page’s browser code without a calculation API request. That does not establish a site-wide privacy guarantee. Read the privacy policy for the website’s separate data practices.
Background: FINRA on automated tool assumptions and limitations; BLS on purchasing power and constant dollars. These sources explain interpretation; they do not validate the example inputs or this simulator’s forecasts.