Monte Carlo Simulator
Run thousands of randomized market paths from your own return and volatility assumptions to see the realistic range of outcomes — not one misleading "average" projection.
Each path draws a fresh sequence of yearly returns from a normal distribution with your mean and volatility, compounds the balance, then applies your contribution: balanceₜ = balanceₜ₋₁ × (1 + r) + contribution, where r = mean + volatility × z. Reproducible seed: 12345. A normal model understates rare crashes and sequence risk — treat this as a study of ranges, not a forecast. Educational only, not financial advice.
Why one number lies to you
A normal projection assumes your money earns the exact same return every single year. Markets never do that. Two portfolios can average the identical return and still end decades apart, because the order of the good and bad years matters — a crash early in retirement does far more damage than the same crash late. That is called sequence risk, and a straight-line calculator can’t show it. A Monte Carlo simulation can: it runs thousands of different possible futures and reports the whole range instead of one comfortable, misleading average.
Take a concrete case: $50K to start, $6K added a year for 30 years, a 7% expected return with 15% volatility. Across 5,000 simulated paths the median ended near $768K — but the unlucky 10th percentile finished around $371K and the lucky 90th near $1.70M. That gap is the point. Planning around only the median quietly ignores the paths where you fall short.
How it works
Each simulated year draws a random return r = mean + volatility × z, where z is a standard-normal draw, then compounds and adds your contribution: balance = balance × (1 + r) + contribution. Set the contribution negative to model a yearly withdrawal and the tool will also report how often the money runs out — the retirement question. Every run uses a printed seed, so the exact result is reproducible.
Honest limitation: this model draws from a normal distribution, which understates the odds of rare crashes (fat tails). Real markets are wilder than the bell curve. Use it to reason about ranges and sequence risk, not to predict a number. Educational only, not financial advice.
Keep going
Want the straight-line version without randomness? Use the compound interest calculator. To turn a start and end value into an annual rate, the CAGR calculator; to judge return against the volatility you assumed, the Sharpe ratio calculator.
Common questions
What is a Monte Carlo simulation?
A Monte Carlo simulation runs thousands of randomized versions of the future instead of one straight line. Each path draws a different sequence of yearly returns from your assumptions, so instead of a single "you will have $X" number you get a realistic range — a 10th, 50th, and 90th percentile — plus the odds of reaching a goal.
Why is that better than a compound-interest projection?
A compound-interest calculator assumes the exact same return every single year, which never happens. Two portfolios with the same average return can end up wildly apart depending on the order of good and bad years (sequence risk). Monte Carlo shows that spread; a straight-line projection hides it.
What return and volatility should I use?
They are your assumptions, not ours. As rough reference points, a broad US stock index has historically returned around 10% a year (about 7% after inflation) with roughly 15–20% annual volatility; a 60/40 stock-bond mix is lower on both. The tool shows the formula so you can check what your inputs imply.
How accurate is it?
Treat it as a study, not a forecast. This model draws returns from a normal distribution, which understates the risk of rare crashes and fat tails, and it cannot know your actual future returns. It is a way to reason about ranges and sequence risk — never a guarantee. Educational only, not financial advice.