A single retirement projection that assumes your portfolio earns exactly 7% every year is a comforting lie. Real markets zig and zag: some years you make 25%, other years you lose 15%, and the order of those returns hits a retiree far harder than someone still saving. This Monte Carlo calculator models the whole distribution of market lifetimes on top of your withdrawal plan, then shows you the spread of possible outcomes — not one best-guess number.
The result card gives you the average final balance, the 5th percentile (pessimistic), the 50th percentile (median), the 95th percentile (optimistic), and the single number that matters most: the probability that you never run out of money.
How to Use
- Enter your Current Retirement Balance — the total invested nest egg on the day you retire. Include 401(k), IRA, taxable brokerage, and any cash you plan to draw from.
- Set your Annual Withdrawal — how much you expect to spend in the first year, in today's dollars. The engine automatically grows this for inflation in later years.
- Choose your Years in Retirement. Thirty years is the default for a 65-year-old; if you plan to retire at 50, enter 40 or 45 to stress-test a much longer runway.
- Type your Expected Annual Return. A balanced 60/40 stock/bond portfolio has historically averaged about 6–7% nominal; an all-stock portfolio runs closer to 10% but with deeper crashes.
- Set your Annual Volatility. This is the standard deviation of yearly returns. A 60/40 mix is roughly 15%; a bond-heavy portfolio is closer to 5%. Higher volatility is what kills retirement plans through the sequence-of-returns effect.
- Optionally adjust Inflation (default 2.5%). It raises your withdrawal each year to keep purchasing power constant.
After you slide the controls, read the Probability of Not Running Out first. Financial planners generally treat 80% as the floor, 90% as comfortable, and 95% as over-conservative. Then scan the percentile range: if the 5th-percentile outcome ends at zero while the median ends with several million dollars, your plan works in most worlds but fails in bad ones — and you can nudge withdrawals down to fix that.
The Formula
Each retired year is modeled as a random return drawn from a normal distribution centered on your expected return μ, with spread equal to your volatility σ:
Bₜ₊₁ = Bₜ × (1 + rₜ) − Wₜ, where rₜ ~ Normal(μ, σ) and Wₜ = W × (1 + infl)ᵗ grows with inflation.
Because the result must load instantly in the browser, the terminal balance over N years is computed in closed form using the lognormal distribution that a Monte Carlo run converges to. Over N independent years the product of (1+rₜ) has mean (1+μ)ᴺ and log-variance N·σ², so the p-th percentile of the ending balance is:
- P(p) = exp( N·(ln(1+μ) − σ²/2) + σ·√N·zₚ ), with z₅ = −1.645, z₅₀ = 0, z₉₅ = +1.645
- Percentile balance = B₀·P(p) − S, where S is the future value of the inflation-growing withdrawal stream
- Expected balance = B₀·(1+μ)ᴺ − S (the single number a flat-return calculator shows)
The Probability of Not Running Out is the share of that distribution that still ends above zero: the funding shortfall is converted to a z-score and passed through the normal CDF (the Abramowitz & Stegun 7.1.26 approximation). A path whose balance ever hits zero is "ruined," so the reported probability is conservative relative to the worst-case tail.
The Sequence-of-Returns Risk
The reason Monte Carlo exists is the sequence-of-returns effect. Two retirees can average the exact same 7% over 30 years and end up in opposite financial conditions. The one who retires into a 40% stock crash in years one and two, while still withdrawing $40,000, is selling depressed shares to pay bills and may never recover. The one who retires into a bull market and crashes in year 25, when the portfolio is already large, sails through untouched.
That is why volatility matters so much in this calculator — and why it is an explicit input. Two plans with the same expected return but 10% versus 25% volatility can show a wide gap in success probability. Cutting your stock allocation modestly, building a cash buffer, or lowering withdrawals by $5,000 a year are the three levers that move the needle.
Examples
Worked example (zero-volatility check). Start with $1,000,000, withdraw $40,000 per year for 5 years, at a steady 5% return and 0% volatility. The closed form gives B₅ = $1,000,000 × 1.05⁵ − $40,000 × ((1.05⁵ − 1)/0.05) = $1,055,256.31. With zero volatility the 5th, 50th and 95th percentiles all collapse to this same number, and success is ~100%.
Example 1 — The classic million-dollar retiree. Starting with $1,000,000, withdrawing $40,000 per year (a 4% initial rate), over 30 years, with a 7% expected return and 15% volatility, the model produces an average final balance of about $3,833,824, a median balance near $1,653,308, a 95th-percentile balance of about $17,203,142, and a success probability of roughly 67%. The 5th-percentile (pessimistic) path ends at $0 — meaning the worst about third of outcomes run dry. This is deliberately conservative: an iid normal model ignores the rebalancing and mean-reversion that helped historical 4% retirees.
Example 2 — The over-spender. Same $1,000,000 but withdrawing $60,000 (a 6% rate) on the same assumptions. The average final balance falls to about $1,944,608, the median balance drops to $0, and success falls to roughly 48% — you run out of money in about half of simulated lifetimes. This is the gap a flat-return calculator would completely hide.
Example 3 — The saver. Dropping the withdrawal to $30,000 (a 3% rate) lifts the average final balance to about $4,778,431, the median to $2,597,916, and success to roughly 79% — a clear illustration of how small cuts in spending buy a large safety margin.
Example 4 — The early retiree. A 52-year-old with $1,500,000 wants $60,000 per year for 40 years at a 6% return, 12% volatility and 2.5% inflation. The longer horizon plus cost-of-living raises pull the average final balance to about $2,398,884, the median path to $0, and success down to roughly 44% — a warning that stretching the plan to 40 years demands either a larger nest egg or a lower withdrawal.
FAQ
What is a good probability of retirement success?
Most Certified Financial Planners treat 80% as the minimum acceptable threshold, 90% as comfortable, and 95% as conservative. Below 80%, you are taking a real risk that you will outlive your money; above 95%, you are likely leaving wealth on the table that you could have spent while you were young enough to enjoy it.
How is this different from a regular retirement calculator?
A normal retirement calculator uses one constant assumed return every year — it tells you what happens in the average world. A Monte Carlo calculator models the full distribution of random return sequences, capturing bad years, crashes, and the sequence-of-returns risk that dominates actual retirement outcomes.
What expected return should I use?
Use a long-run backward-looking average, not a rosy forward guess. A 60% stock / 40% bond portfolio has historically returned about 6–7% nominal, while an all-equity portfolio runs closer to 9–10%. Plug 7% as a middle-of-the-road baseline, then test 5% and 9% to see the range.
What volatility number is realistic?
Annual volatility is the standard deviation of yearly returns. A broad US stock index is around 16–20%; a 60/40 balanced fund is roughly 10–15%; an all-bond portfolio is 3–5%. Leave the default 15% if you hold a typical balanced retirement account.
Why does my success rate change so much when I raise my withdrawal by $10,000?
Because withdrawals come out of a volatile pool. A slightly higher withdrawal forces you to sell more shares in down years, permanently shrinking the base that needs to recover. Monte Carlo captures this compounding damage; a flat-return calculator makes raising spending look nearly free.
Why is the 5th-percentile balance showing $0?
A $0 pessimistic balance does not mean an error — it means that in the worst about half of return sequences the portfolio hits zero before the horizon. That is the single most useful output on the card: it tells you the plan fails in bad worlds, and cutting the withdrawal $5,000 is usually the cheapest fix.
Does this calculator include taxes and Social Security?
No. The withdrawal you enter should be your gross portfolio draw; layer your own tax rate and guaranteed income (Social Security, pensions, annuities) on top. If Social Security covers a large chunk of expenses, your portfolio withdrawal is effectively smaller and your success rate rises.
Disclaimer
This Monte Carlo calculator is provided for informational purposes only and does not constitute financial, investment, tax, or retirement advice. Results rely on the inputs you enter and on the assumption that future returns follow a lognormal distribution around your chosen mean and volatility; real markets can suffer longer or deeper drawdowns, and sequence-of-returns risk is only approximated by the closed-form model. Past performance is not a guarantee of future results. Always build your retirement plan with a fiduciary financial advisor before making withdrawal or allocation decisions.