Calculator
Monte Carlo Simulation Calculator
Monte Carlo Simulation Calculator
Median Ending Balance
$801,777.32
Simulation Analysis
In 300 simulated market paths, your $100,000 plus $6,000 of annual contributions has a 10% chance of ending below $391,501.2, a 50/50 shot at landing near $801,777.32, and a 10% chance of reaching $1,686,051.69 or better after 25 years. The spread between those outcomes is market volatility at work — the average result is only the middle of a wide range, not a promise.
*Simulated outcomes assume lognormally distributed annual returns with a constant mean and volatility. Past distributions do not guarantee future results. This tool is educational only, not financial advice.
Why a Single Forecast Is Not a Plan
Every compound-interest calculator promises one number: grow $100,000 at 7% for 25 years and you get $542,743. But markets do not hand out fixed annual returns. The real path wanders — some years up 20%, some years down 30% — and a single forecast hides exactly the risk you need to manage. A Monte Carlo simulation replaces that single number with hundreds of plausible market histories, each drawn from the same average return and volatility you expect, and reports the full range of where you could land. For US investors this matters because the two biggest financial decisions of a lifetime — how much to save for retirement and how fast to spend it — hinge on tail outcomes, not averages. The classic research behind the 4% rule was built on exactly this idea: test a withdrawal plan against thousands of market sequences and require it to survive nearly all of them. Today the technique has trickled down from pension consultants to free web tools, and it has become the standard sanity check before committing to any retirement income plan or any big savings target.
Rolling the Dice 300 Times
Each simulated year the calculator draws one random return from a normal distribution centered on your expected annual return with your chosen volatility, converts it to a compounded annual growth via exp(μ − σ²/2 + σz) — the standard lognormal price model used in finance — applies it to the balance, adds annual contributions, and subtracts any withdrawal. This repeats for the full horizon, and the whole story is replayed 300 times with fresh random draws. From the 300 ending balances the tool reads off the percentiles: the median (50th) is the middle-of-the-road outcome, the 10th percentile is the unlucky-but-plausible one, and the 90th is the lucky one. For withdrawal plans it also counts how many of the 300 paths ended with money still in the account — that survival share is the probability the plan lasts. The −σ²/2 term in the drift matters: it keeps the average of many compounded random paths equal to your stated expected return instead of quietly inflating it. Because every run uses a pseudo-random generator, the results are reproducible per seed, and the Re-run button draws a fresh batch so you can see how much the percentiles themselves vary.
Expert Insights
Volatility Shrinks Your Compounded Return
A portfolio averaging 7% with 15% volatility compounds closer to 6% per year on a dollar-weighted basis, because big drawdowns take disproportionate percent gains to recover. The wider the volatility you assume, the further the median drifts below the headline average. When stress-testing a plan, raising volatility by five points is often more honest than cutting the expected return.
Sequence Risk Only Hurts When You Spend
While accumulating, a bad early year is nearly free — you keep buying cheap shares and recover with time. The moment withdrawals begin, the same bad year becomes permanent damage, because you sell shares at the bottom. That asymmetry is why a 4% withdrawal rate that survives 95% of paths can still be the right call, and why the simulator reports survival probability separately from ending balances.
Calibrate Your Inputs to a 60/40, Not a Fantasy
Long-run US large-cap history suggests roughly 9–10% nominal return with about 15% volatility; a balanced 60/40 portfolio has returned about 8% with roughly 11%. Plugging 12% returns and 5% volatility into a simulator produces reassuring output that says nothing about your actual portfolio. Start from a realistic mix, then adjust expectations if your allocation is more aggressive or more conservative.
Actionable Tips
- 1
Plan on the 10th Percentile, Not the Median
Treat the median outcome as the ceiling of your base plan and the 10th percentile as its floor. If the plan fails on the unlucky path — the retirement ends early or the target is missed — add contributions or cut withdrawals until it survives there too.
- 2
Aim for 90%+ Survival on Withdrawal Plans
Retirement planning literature generally treats 90–95% survival across simulated histories as the safety bar for income withdrawal. Below 80% you are effectively betting that your retirement avoids a repeat of 2000–2002 or 2008–2009.
- 3
Re-run After Every Big Life Change
Salary jumps, market rallies, and rate changes all move your odds. Re-run the simulation at least yearly and after any change of more than 10% in balance or contribution — the numbers that justified your plan can drift quietly without it.
Real-World Examples
Maya's Retirement Wake-Up Call
Maya, 52, assumed her $400,000 would grow straight-line at 7% to funding her $30,000-a-year retirement at 62. A deterministic spreadsheet agreed. But this simulator showed that with 15% volatility, the 10th percentile ended her plan broke at 74. She increased her savings rate by $400/month and delayed retirement one year, pushing survival over 92%.
The FIRE Couple's Margin Test
Jordan and Sam were leaving jobs at 38 with $1.05 million and wanted to spend $42,000 a year — exactly 4%. The simulation survived 91% of 300 paths over 50 years, but the 10th percentile ran dry at 79. They kept the 4% draw but wrote a guardrail rule: cut spending 10% in any year the portfolio fell 25%, which their plan review confirmed would have covered nearly all the failing paths.
A Realistic Target for a Young Saver
Chris, 27, wanted to know if $300/month for 35 years could realistically reach $1 million. The deterministic answer said $519,000. Across 300 paths, hitting $1 million required landing in roughly the top 5% of outcomes. He saw clearly that doubling contributions — not luck — was the lever, and his new plan put the median outcome right at his target.
Glossary of Terms
- Monte Carlo Simulation
- A modeling technique that runs hundreds or thousands of randomized scenarios sharing the same average and volatility, then reports the distribution of outcomes instead of a single forecast.
- Percentile
- A rank in a sorted list of outcomes — the 10th percentile is the result only 10% of simulated paths fell below, the 50th (median) is the middle outcome.
- Volatility
- The standard deviation of annual returns around the average — a statistical measure of how violently a portfolio's value swings year to year.
Frequently Asked Questions
Everything you need to know about this topic.
Ivy Sinclair-Wren
Financial Chaos Analyst
Ivy Sinclair-Wren is a Financial Chaos Analyst covering investing, AI, wealth psychology, and the emotional consequences of opening finance apps during market crashes. Based in Melbourne, she specializes in demystifying the US tax code and helping users navigate the intersection of spreadsheet logic and human irrationality.