Monte Carlo Retirement Simulator
Withdrawing 40,000 a year (rising with inflation) from 1,000,000 for 30 years, with a 7% expected return, 12% volatility and 2.5% inflation, the money lasts in 82% of 10,000 simulated paths. This is a model estimate, not a guarantee.
How to use
- Enter your savings today, the yearly amount you plan to spend in retirement (or a withdrawal rate) and how many years it has to last.
- Set the expected yearly return, its volatility (standard deviation) and inflation. Say whether the return already has inflation taken out (real) or not (nominal).
- Optional: if you are still saving, add the years until retirement and how much you add each year.
- Read the success rate, the percentile chart and when the failed paths ran out. Change any input and the 10,000 paths are run again.
How it works
Each year the portfolio earns a random gross return 1 + R drawn from a lognormal distribution whose mean is 1 + the expected return and whose standard deviation is the volatility you enter: σ² = ln(1 + s² ÷ (1 + m)²) and μ = ln(1 + m) − σ² ÷ 2. Normal draws come from the Box-Muller transform on a seeded random number generator, so the same inputs always give the same result.
Everything is shown in today's money. A nominal return is converted to real with (1 + nominal) ÷ (1 + inflation) − 1, and its volatility is divided by 1 + inflation. Inflation is a fixed rate, not random.
Saving years: balance × (1 + R) + yearly contribution, added at the end of each year. Retirement years: the withdrawal comes out at the start of the year, then the rest earns (1 + R). If the balance cannot cover the full withdrawal, that path has run out in that year and counts as a failure.
With a withdrawal rate, the first withdrawal is that percentage of the balance on the day you retire in each path. With inflation adjustment off, the first year's amount stays fixed in dollars, so its real value falls by the inflation rate every year.
The success rate is the share of 10,000 paths that never ran out. The chart shows, for each year, the balance that 10%, 50% and 90% of paths were below. The 4% rule line runs the same paths with a first withdrawal of 4% of the retirement balance, raised with inflation, which is the rule from Bengen (1994) and the Trinity study.
Check: with volatility set to 0 the result matches the annuity-due formula exactly. The balance after n years is B·g^n − W·g·(g^n − 1) ÷ r, with g = 1 + r, and the largest withdrawal that lasts n years is B·r ÷ ((1 + r)(1 − (1 + r)^−n)).
Sources: Bengen, Determining Withdrawal Rates Using Historical Data (1994) · Cooley, Hubbard, Walz, Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable (1998) · Box and Muller, A Note on the Generation of Random Normal Deviates (1958)Last reviewed 2026-10-16
FAQ
What success rate should I aim for?
Many planners look for roughly 80% to 95%. A 100% result usually means you are spending less than you could. A lower rate does not mean you will go broke; it means that in some bad market sequences you would need to cut spending or earn some income.
Does the 4% rule still work?
Bengen (1994) found that 4% of the starting balance, raised with inflation, lasted at least 30 years in every historical US period he tested with a stock and bond mix. The Trinity study (Cooley, Hubbard and Walz, 1998) reported similar results. Those are past US returns. This simulator lets you test the rule against the returns you assume instead.
What expected return and volatility should I use?
Use long-run figures for your actual mix of stocks and bonds, after fees if you can. A balanced portfolio is often modeled at about 5% to 7% nominal with 10% to 12% volatility, and an all-stock one at 7% to 10% with 15% to 20% volatility. Small changes in the return move the result a lot, so try a pessimistic case too.
Real or nominal return, which one do I enter?
Either, as long as you pick the matching option. Nominal is the headline return before inflation. Real has inflation removed already. If you choose real, the inflation input only affects withdrawals that are not inflation-adjusted.
What are the limits of this model?
Returns are lognormal and independent from year to year, so the model has no fat tails, no crashes beyond what the volatility implies, no momentum and no mean reversion. Inflation is constant. Taxes, fund fees, Social Security or pensions, and spending changes in later life are not included. Use it to compare plans, not as a forecast.
Why does the result change when I change the seed?
The seed picks a different set of 10,000 random paths. With 10,000 paths the success rate usually moves by less than one percentage point between seeds, which is the sampling error of the simulation.