The Financial Life Simulator, Explained
After reading this you will understand how a Monte Carlo life simulation works, why it draws a fan of outcomes instead of a single line, and how to read the success rate without fooling yourself.
What the simulator does and why one number lies
Most retirement math gives you a single answer. You save some amount, assume a return like 6% a year, and the spreadsheet projects a smooth curve to a tidy final balance. That curve is honest about arithmetic and dishonest about life. Real markets do not deliver 6% every year. They deliver 22%, then minus 18%, then 9%, then minus 4%, in an order nobody can predict.
The Financial Life Simulator replaces the single curve with a thousand curves. Each one is a plausible history: a different sequence of stock returns, bond returns, inflation, and the occasional crash. Your career, your house purchase, your children, and your retirement date stay fixed across all thousand runs. Only the market changes. The result is a fan chart that shows the median path down the middle, a lucky 90th-percentile path near the top, and an unlucky 10th-percentile path near the bottom.
Here is the hook. Suppose two people both average 6% over 30 years. One gets a crash in year 2, the other gets the same crash in year 28. On paper they earned the same average. In practice, if they are drawing income the whole time, the early-crash person can run out of money and the late-crash person retires comfortably. A single average projection cannot show that gap. A fan chart shows it as the distance between the top and bottom edges.
When to use it, and when not to
Use the simulator when the question is about risk and range, not a precise target. Good questions: "How likely is it that my money outlasts me?" "How much does retiring at 60 instead of 65 widen the unlucky case?" "If I take a two-year career break at 35, does the 10th-percentile path still recover?"
Do not use it as a tax engine or a government-benefit calculator. As the tool footnotes say, taxes, pensions, and benefits vary too much by country to model in detail. Treat every number as a planning sketch.
If you want a single crisp target number rather than a range, other tools fit better. The Retirement Savings Calculator gives a balance at retirement and the income it supports. The FIRE Calculator gives your independence number and years to reach it.
The math, from the ground up
Each simulated year the portfolio grows by a random return and shrinks by any withdrawal. The core update is one line:
Here W_t is your net worth at the start of year t, C_t is what you contribute that year, S_t is what you spend from the portfolio, and r_t is that year's total return. Before retirement S_t is usually zero and C_t is positive. After retirement it flips.
The return itself is drawn at random. A simple model treats each year as a draw from a normal distribution:
Here \mu is the expected return and \sigma is the volatility, both scaling with your equity share. A 100% stock mix might use \mu = 0.07 and \sigma = 0.18. A 40% stock mix might use \mu = 0.045 and \sigma = 0.09. The term z_t is a standard random shock: about two-thirds of the time it lands between -1 and 1, and it occasionally reaches -3, which is the crash.
Inflation is simulated on its own so that spending needs and real net worth both grow. Run the update above for every year of your life, repeat the whole life 1,000 times, and sort the ending values. The success rate is simply the fraction of those 1,000 lives where W_t never fell below zero after retirement.
A worked example with the demo data
One life, then a thousand
Start with the tool defaults and follow a single simulated year to see the arithmetic, then imagine it repeated. Say the defaults put you at age 40 with 200000 saved, contributing 15000 a year, still working.
- Start of year: W_t = 200000.
- Add the contribution and subtract spending:
200000 + 15000 - 0 = 215000. - Draw a return. Suppose this run pulls z_t = 0.5 with \mu = 0.06 and \sigma = 0.15, so r_t = 0.06 + 0.15 \cdot 0.5 = 0.135.
- Apply it: W_{t+1} = 215000 \times 1.135 = 244025.
The next year draws a fresh z_t. One run might draw -2.1 in year three, cutting the balance hard. Another run draws only mild years and glides upward. After 50 years you have one full net-worth path. Do this 1,000 times and sort the endings.
The table below shows how a spread of single-year returns builds the fan. These are illustrative percentiles for a mixed portfolio.
| Percentile | z value | Return that year |
|---|---|---|
| 10th (unlucky) | -1.28 | -8.58% |
| 50th (median) | 0.00 | 5.50% |
| 90th (lucky) | 1.28 | 19.6% |
Reading the fan chart
The fan chart plots net worth by age. The three lines are percentiles of the 1,000 runs, computed separately at each age. The median line is not any single life. It is the middle value at every age, stitched together.
Watch three features. First, the fan widens with age because randomness compounds. Second, life events bend all three lines at once: a house purchase drops them by the deposit, children raise spending for two decades, retirement flips contributions to withdrawals. Third, the gap between the median and the 10th percentile at your oldest age is the real risk you carry. If the median ends at 500000 but the 10th percentile hits zero at 82, a comfortable median hides a one-in-ten chance of running dry.
Sequence-of-returns risk, made visible
This is the reason the fan exists. Consider two retirees, each starting with 1,000,000, each withdrawing 50000 a year, each earning the same set of returns but in opposite order.
Retiree A hits a 30% crash in year one. The portfolio falls to 700000, then the 50000 withdrawal takes it to 650000. Even strong later years struggle to rebuild from that low base. Retiree B gets the good years first, grows to 1,300,000, and easily absorbs the same crash when it arrives at year 20. Same average return, very different endings.
A single average projection cannot show this. It bakes in one smooth return and always survives. If a calculator tells you a 4% withdrawal "works" with no mention of the unlucky tail, it is hiding the case that actually threatens you.
Common mistakes
The most frequent error is reading only the median. The median is the outcome you beat half the time. Planning your retirement on it means planning to fall short in half of all futures. Read the 10th-percentile line as your stress test.
The second mistake is chasing a 100% success rate. Pushing from 90% to 99% usually means saving far more or spending far less than a real life allows. A 90% success rate over a 30-year retirement is often a reasonable target, because you can adjust spending along the way rather than freezing it on day one.
The third mistake is treating volatility as free lunch to be dialed away. A high equity share raises both \mu and \sigma. That lifts the median and the 90th percentile, and it also drops the 10th percentile. More stocks make good outcomes better and bad outcomes worse. The fan gets taller, not just higher.
Related tools
The simulator answers "what is the range." Sharper single-number questions have their own tools. For portfolio depletion under inflating withdrawals, see How Long Will My Money Last?. For the savings that will grow to your target on their own with no further contributions, see the Coast FIRE Calculator. To value a stream of fixed payments as a present sum, use the Annuity Value Calculator, and to see the monthly income a lump sum can buy, the Annuity Payout Calculator.
Frequently asked questions
What does the success rate actually count?
It is the share of the 1,000 simulated lives in which your net worth never hit zero after retirement. A 90% success rate means 900 of 1,000 lives survived to the end and 100 ran out at some point.
Why do the results change every time I move a slider?
They rerun the full thousand lives with fresh random draws. Small wiggles in the success rate between runs are sampling noise, not a real change. A shift of 1 or 2 percentage points from redrawing is normal; a 10-point shift means your input genuinely mattered.
Is more stock always better?
No. A higher equity share raises the expected return and the volatility together. The median and lucky paths rise, but the unlucky 10th-percentile path can fall. Look at the bottom of the fan, not only the middle, before deciding.
Why ignore taxes and pensions?
They differ so much by country and by individual that a general model would give false precision. The results are a planning sketch. A qualified adviser can layer your actual tax and benefit situation on top.
Does my data leave my device?
No. The simulations run entirely in your browser. Nothing you enter is sent anywhere.
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