Monte Carlo Investment Calculator

How to use this calculator

Enter your starting investment, monthly contribution, expected annual return, and volatility (standard deviation). Then hit Run 1,000 Simulations.

The calculator draws 1,000 random annual returns from a normal distribution and compounds each one year by year. Every simulation produces a different final portfolio value. The output is a range of outcomes, not a single number.

Expected Annual Return is your assumed long-run average. 7% is a reasonable estimate for a diversified equity portfolio in real terms. Don’t use nominal returns without accounting for inflation; they inflate your outcome estimates.

Volatility (Std Dev) is how much returns swing around that average. The S&P 500 has a standard deviation of about 15% to 17% annually. Bonds run 5% to 8%. A 60/40 portfolio lands around 10% to 12%.

Target Portfolio Value is optional. Enter your FIRE number, retirement target, or any goal. The calculator tells you what percentage of simulations reached it: your probability of success.

Why a single projection number lies to you

Every standard retirement calculator gives you one figure. “At 7% for 30 years, you’ll have $1.4 million.” Clean, simple, useless.

The stock market doesn’t return 7% every year. It returned 32% in 2013, then dropped 37% in 2008. The sequence matters enormously. Two portfolios with identical average returns can produce completely different results depending on when the bad years hit.

A fixed-rate projection assumes smooth, predictable growth. Monte Carlo assumes nothing of the sort. It forces every investor to confront an uncomfortable truth: your outcome isn’t a number, it’s a distribution.

The difference matters for decision-making. Knowing your median outcome is $2.1M tells you one thing. Knowing your 10th percentile outcome is $800,000 tells you something more useful: what you need to plan around to avoid running out of money.

How the simulation works

Each simulation runs year by year, drawing a random annual return from a lognormal distribution.

The μ − σ²/2 term is the drift adjustment. Without it, the simulation would be systematically optimistic. Lognormal distributions have a mean above the median when volatility is large. The adjustment pins the expected geometric return to your input.

After each year’s return, the simulation adds your annual contribution and floors the balance at zero (you can’t lose more than you have).

1,000 simulations × 30 years = 30,000 random return draws. The results are sorted. The 5th percentile is the value exceeded by 95% of simulations. The 95th percentile is exceeded by only 5%.

The Box-Muller transform generates normally distributed random numbers from uniform random inputs, which is what makes the simulation computationally feasible in a browser without a statistics library.

What the percentile bands actually mean

5th percentile: 95% of simulations ended above this. You’d need a genuinely terrible run of luck: think 2000 to 2009 compounded, where the S&P 500 returned roughly negative 0.9% annually over the decade, to land here.

25th percentile: Below-average markets. Bad years at the wrong time, lackluster recoveries. A rough but survivable outcome.

50th percentile (median): Half ended above, half below. This is your central planning estimate, not a guarantee. Markets are roughly as likely to be worse as they are to be better.

75th percentile: Good conditions. Markets cooperated, returns were above average for most of the horizon.

95th percentile: An exceptional run. Don’t plan for this. Be glad when it happens.

When planning for retirement, build your spending plan around the 10th to 25th percentile, not the median. That buffer is what keeps you solvent when markets don’t cooperate. The difference between planning from the median and planning from the 25th percentile might be $300 more per month in contributions or 2 more years of work. That’s a modest price for significantly better protection.

Probability of success: what it really tells you

A 75% probability of success means 750 of 1,000 simulations reached your target. The other 250 didn’t.

That number answers a concrete question: if you started saving with these inputs in 1,000 parallel universes with randomized market conditions, how many of those versions of you reach the goal?

Most financial planners target 80% to 90% for retirement goals. Here’s a rough framework:

The most valuable use of success rate: change one variable and see what happens. What does an extra $300 per month do? What if you delay retirement by 2 years? What if volatility is 17% rather than 15%? The calculator quantifies trade-offs instead of leaving them as guesswork.

Volatility drag: why the median is lower than you’d expect

At 7% average return and 15% volatility, the median portfolio outcome is less than what a simple compound interest calculator would predict.

The reason is arithmetic. A 50% gain followed by a 50% loss doesn’t get you back to where you started. It leaves you at 75% of your original balance. The average of +50% and -50% is 0%, but the geometric result is -13.4%.

That 1.1% gap compounds significantly. Over 30 years, a $500 per month contribution at 5.875% reaches about $487,000 versus $580,000 at 7%. The difference is pure volatility drag.

This is why the Monte Carlo median looks “pessimistic” compared to a basic calculator. It’s accurate, and the basic calculator is misleading. The basic calculator assumes no volatility. Real markets have substantial volatility.

Sequence of returns: the retirement killer

Volatility drag matters during accumulation. Sequence of returns risk is what can destroy a retirement.

The order in which returns arrive matters enormously once you’re withdrawing. A major crash in year one of retirement forces you to sell at the bottom. You withdraw from a depleted portfolio, leaving less to recover when markets bounce back.

Run the same simulation twice with identical average returns but different sequences and the outcomes can diverge by hundreds of thousands of dollars. The simulation captures this because each run draws a random sequence, not just a random average.

Two retirees. Both earn 7% average over 30 years. One retires into a bull market, one into a crash. The one who retired into the crash might run out of money. The other ends up with more than expected. Monte Carlo assigns each a different simulation number, and the spread between their outcomes is exactly what the 5th and 95th percentile bands represent.

This is why controlling the withdrawal rate matters more than expected return during retirement. A 3.5% withdrawal on a $2M portfolio ($70,000/year) survives nearly every Monte Carlo sequence at reasonable return assumptions. A 6% withdrawal ($120,000/year) fails in many of them.

Historical volatility reference

Use these figures to calibrate your volatility input:

These are long-run historical averages. Individual decades deviate substantially. The 1970s produced near-zero real returns on US equities. The 1990s produced around 18% nominal annually. The simulation draws from the distribution. It doesn’t know which decade you’re in.

If you’re using real (inflation-adjusted) targets, subtract 2.5% to 3% from the expected return inputs above.

Limitations worth knowing

Normal distribution assumption. Real markets have fat tails. Crashes happen more often and more severely than a normal distribution predicts. The 2008 financial crisis and the March 2020 COVID crash were both statistically implausible under a normal model. The simulation underestimates extreme tail risk.

Independent returns. Each year’s return is drawn independently. In reality, bad years cluster during recessions. The model can underestimate sequence risk because it doesn’t replicate multi-year bear markets.

Static contributions. The model assumes you contribute the same amount every month. Real life involves job changes, layoffs, raises, and periods of zero savings.

1,000 simulations. Professional software uses 10,000 or more. At 1,000 runs, probability estimates are accurate to within about 1.5% to 2%. Sufficient for planning decisions, but rerun a few times if you want to see how stable the numbers are.

Despite all of this, Monte Carlo is far more useful than a single projected number. Use it to understand the range, then make conservative planning decisions that survive the left tail of that range.

How to use Monte Carlo results to make real decisions

The simulation output becomes useful when you treat it as a decision tool rather than a prediction.

Evaluating contribution changes. Run the simulation with your current contributions. Note the probability of success. Add $300 per month and run again. If success rate jumps from 68% to 79%, that $300 per month is worth approximately 11 percentage points of retirement security. You can make a conscious choice about whether that trade-off (less spending now, higher success rate) is worth it.

Evaluating retirement timing. Run the simulation targeting age 60, then age 62, then age 65. The success rate typically improves by 5 to 10 percentage points per additional 2 years. If you’re at 70% targeting 60 and 88% targeting 63, those three years of additional work are worth 18 points of security. Some people find that trade-off easy. Others find it unacceptable. The calculator makes the trade-off visible rather than forcing a guess.

Stress-testing your plan. Run the simulation with higher volatility (say, 20% instead of 15%) to simulate a more concentrated or risky portfolio. Run it with a lower expected return (5% instead of 7%) to simulate a poor-return decade at the start. If your plan survives these stress tests at acceptable probability, it’s robust. If it fails, you know where the vulnerabilities are.

Setting a contribution floor. Find the minimum monthly contribution that keeps your success probability above your target threshold (say, 85%). Treat that as your contribution floor. In good income years, contribute more. In lean years, hit the floor. This approach ensures you’re always building toward the target even when life gets difficult.

The most powerful use of Monte Carlo isn’t the single result you get from one run. It’s the pattern you see when you run it across 10 different scenarios, systematically varying the key inputs to understand what your retirement is actually sensitive to.