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Monte Carlo simulator: the spread, not the single line
Play your savings forward thousands of times with returns drawn from the long-run record of world markets. See a low, median and high outcome, and how often the money lasts once you live off it. Everything runs in your browser; nothing is sent to a server.
After 30 years of saving
Low and high: 1 in 10 paths ended below or above (the 10th and 90th percentiles). Median: half ended above, half below.
A calculator with one fixed return would draw a single line to €970,833. 44% of the simulated paths ended below it.
These are shares of 10,000 simulated paths, not the chance of anything happening to you. The model is a simplification; see what it leaves out below.
Show the numbers as a table
| Year | Low (10th) | Median | High (90th) | Single line |
|---|---|---|---|---|
| 0 | €50,000 | €50,000 | €50,000 | €50,000 |
| 5 | €98,748 | €132,426 | €180,130 | €130,387 |
| 10 | €163,045 | €238,925 | €361,727 | €231,425 |
| 15 | €235,527 | €374,223 | €615,036 | €358,420 |
| 20 | €321,559 | €550,163 | €969,435 | €518,040 |
| 25 | €423,945 | €769,675 | €1,472,880 | €718,666 |
| 30 | €547,008 | €1,058,721 | €2,163,515 | €970,833 |
The nidhi planner runs this kind of simulation on your whole picture: every account in its own currency, your income and spending over time, and the events you are planning for.
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How it works
- Each simulated year draws a stock return and a bond return, after inflation. Their averages and swings match world markets from 1900 to 2025: stocks 6.8% a year on average with a standard deviation of 17.3%, bonds 2.3% with 11.2%. The two are mildly linked (a correlation of about 0.2). That link has swung widely over history, positive and negative, so this is a simplification. "Cautious" and "Optimistic" keep these swings and move the compound return to stocks 4% or 6% a year and bonds 1% or 3%.
- Your portfolio earns the blend of the two at your chosen mix, rebalanced once a year, less your yearly fees. The year's return is spread evenly over its twelve months.
- Your monthly saving goes in at the start of each month. If you switch on withdrawals, a twelfth of the yearly amount comes out each month after the saving years end. A path that hits zero stays at zero.
- This repeats as many times as you choose, 10,000 by default. The chart shows where the paths fall each year: the shaded bands hold the middle 8 in 10 and the middle half of them.
- The same inputs always give the same result, so a shared link shows exactly what you saw.
Sources: Elroy Dimson, Paul Marsh and Mike Staunton, “Global Markets over the Last 126 Years” (Exhibits 11.3 and 11.5, from the DMS Database), and Edward F. McQuarrie, “US Stocks and Bonds before 1926” (Exhibit 10.4), in Exponential Wealth: Centuries of Stock and Bond Returns, CFA Institute Research Foundation, 2026.
Frequently asked questions
What is a Monte Carlo simulation?
Instead of assuming one fixed return every year, it plays your plan forward thousands of times (10,000 by default), each time with a different random sequence of good and bad years. The result is a spread: what a low, a median and a high outcome might look like. It shows how much the outcome can vary, which a single line hides.
Where do the return assumptions come from?
From the long-run record of world stock and bond markets, 1900 to 2025, compiled by Dimson, Marsh and Staunton and reprinted in Exponential Wealth (CFA Institute Research Foundation, 2026). After inflation, world equities averaged 6.8% a year with a standard deviation of 17.3%, and world bonds 2.3% with 11.2%. The "Historical" setting draws yearly returns from a distribution with those averages and swings. "Cautious" and "Optimistic" keep the same swings but set the compound yearly return to the low and high ends of the long-run range used across nidhi's articles: stocks 4% or 6% a year after inflation, bonds 1% or 3%. No historical series is copied into the tool.
How many paths should I run?
10,000 is plenty: going up to 100,000 usually moves the low, median and high figures by a few percent at most, and takes noticeably longer, especially on a phone. Fewer paths show how far a small sample can drift: with 100, the figures can be several percent away from what thousands of paths give.
How are fees handled?
As a yearly percentage of the balance, taken off every year's return, from 0 to 5%. Use the total of your fund's ongoing charge and any platform fee. Fixed fees and one-off charges are not modelled.
Why is everything in today's money?
All returns are real returns, after inflation. A result of 500,000 means 500,000 of today's purchasing power, so you can compare it directly with prices and salaries you know. It also means your monthly saving and yearly withdrawal stay constant in real terms, which is roughly what happens if you raise them with inflation.
What does "the money lasted in 8 in 10 paths" mean?
Of all the simulated paths, 8 in 10 paid every withdrawal in full for all the years you chose. It is not an 80% chance that your plan works: the model leaves out taxes, changes in your spending, and the real world can be worse (or better) than any model. Treat it as a way to compare plans, not as a promise.
Why does the single line sit above most paths?
Volatility costs compounding: a 20% loss needs a 25% gain to get back to where you were. So a plan that averages a given return with ups and downs usually ends below the same plan with that return every year. The single line uses the compound rate, which is already lower than the simple average, and still close to half the paths end below it.
Is my data sent anywhere?
No. The simulation runs in your browser and the numbers you type are not sent to us or anyone else. Nothing goes into the page address while you use the tool. When you press "Copy a link to this plan", your values go into the link after the # sign, a part of the address browsers never send to a server, and the page removes them from the address bar before analytics start.
Is this financial advice?
No. It is an educational model of one portfolio. It cannot tell you what to invest in, how much to withdraw, or when you can retire.