How to use the retirement monte carlo simulator
- Enter your savings at retirement, the first-year withdrawal, and how much the withdrawal grows each year.
- Enter an average yearly return and a volatility. These are assumptions you choose. Set the volatility to zero to remove the randomness.
- Choose the number of simulated paths and a seed. The same seed always gives the same answer.
- Read the success rate, the balances at selected years and the year in which plans that fail run short.
Formula
each year: withdraw w = w0 x (1 + g)^(t - 1) at the start; if the balance is less than w the path has run short
balance = (balance - w) x exp(mu + sigma z), with z a standard normal draw
sigma^2 = ln(1 + s^2 / (1 + m)^2), mu = ln(1 + m) - sigma^2 / 2
success rate = paths that paid every withdrawal / paths; standard error = sqrt(p (1 - p) / paths)
The lognormal return has exactly the average m and standard deviation s you entered, and a return can never fall below minus 100 percent. Normal draws come from a seeded generator using the Box-Muller method.
1,000,000 with a 40,000 first withdrawal
With savings of $1,000,000, a first withdrawal of $40,000 rising 3% a year, an average return of 6%, a volatility of 12% and 30 years, 10,000 paths with seed 2026 pay every withdrawal in 62.5% of cases. The standard error is about 0.48 percentage points. The median ending balance is $453,893.82, and among the paths that fail the median shortfall comes in year 25.
With no volatility the same plan ends at $1,056,554.61 every time, which is what the Retirement Withdrawal Calculator shows for the same inputs. The gap between $1,056,554.61 and a 62.5% success rate comes from the spread of returns, which the single average hides.
Why the order of returns matters
Withdrawals take a fixed amount from the portfolio whatever it is worth. A bad year early on leaves less to recover when markets return, while the same bad year late in retirement does much less harm. The average return is the same in both cases, but the outcomes are not, and a single-rate projection cannot show it.
The simulation draws returns independently each year with the average and volatility you give. That is a simplification: real returns can be linked from year to year, and their extremes are often larger than a lognormal curve suggests.
Reading the result with care
A success rate is the share of simulated paths that paid every withdrawal. A higher rate is not a guarantee, and a lower one is not a prediction of failure. Change the seed to see the noise: the standard error tells you how much one run can differ from the true value of the model.
The percentiles show a range of outcomes. The tenth percentile balance is 0 in the example, because more than one in ten paths ran short. See how the order of returns affects a plan in the Sequence of Returns Risk Calculator.
Assumptions and limits
- The average return and volatility are examples you replace, not forecasts. Use figures after fees and inflation as you intend to treat them.
- Withdrawals grow by a fixed percentage and are taken at the start of each year. Taxes, pensions and other income are not modeled.
- Paths are limited to 20,000 and years to 60. Percentiles use the nearest rank.
- This is informational and does not give financial advice.
- Nothing typed here leaves your browser.
Frequently asked questions
Why does the same seed give the same answer?
The random numbers come from a fixed formula, so the same seed produces the same sequence of draws. It makes results repeatable and lets you share a link that shows exactly what you saw.
How many paths are enough?
More paths reduce the noise in the success rate. At 10,000 paths the standard error is under half a percentage point for most plans, which is small compared with the uncertainty in the assumptions.
What does it mean when volatility is zero?
Every path earns the average return every year, so all paths are identical and the result matches a plain projection. It is a good way to check the setup against another calculator.
Why is the median balance lower than the projection?
The lognormal median grows more slowly than the average because large gains and losses do not cancel. Withdrawals also lock in losses, which makes the median path end below the single-rate projection.