Monte Carlo Retirement Calculator

What this calculator does

The Monte Carlo Retirement Calculator tests whether your retirement plan survives real-world market variability, not just the average case. Instead of asking "what happens if I earn 7% every year for 30 years?" (which is the deterministic projection most retirement tools run), it asks "what happens if I run my plan against 2,000 different randomly-generated sequences of annual returns, and how often does the money last?"

The simulation models your portfolio year by year: each year, the calculator subtracts your withdrawal, then applies a randomly-chosen annual return drawn from a normal distribution centered on your expected average return with the volatility (standard deviation) you specified. After 2,000 trials, it reports the percentage of paths where your balance stayed positive for the full retirement period, your success rate, plus the median ending balance across all trials.

A 90%+ success rate is generally considered a safe target. Between 75% and 90% means the plan is fragile: a few unlucky sequences of early bad returns could deplete your savings. Below 75% suggests your withdrawals are too aggressive, your time horizon is too long for the portfolio size, or you need to plan for additional income sources. This calculator runs the entire simulation in your browser, no data is sent to a server, and no signup is required.

The formula

Each trial runs a discrete-time simulation across N years. At the start of year y, the balance is B_{y-1}. The year's withdrawal is subtracted first, then the remaining balance grows by a randomly-drawn annual return:

For each year y from 1 to N:
    B_y = (B_{y-1} - W) * (1 + R_y)
    if B_y <= 0: B_y = 0, end trial (failure)
where:
    W = annual withdrawal
    R_y = mu/100 + (sigma/100) * Z_y
    Z_y = standard normal random variable (Box-Muller transform)
    mu = expected mean annual return (%)
    sigma = annual return standard deviation (%)

The random return for each year is drawn independently. This is the standard geometric Brownian motion (GBM) approximation used in finance textbooks, with the caveat that real markets are not strictly lognormal, they exhibit fat tails and volatility clustering that a normal distribution understates.

Why the order of returns matters: A 7% average return with 15% standard deviation can produce sequences that range from roughly -23% to +37% in any single year. If you experience several negative years early in retirement, your portfolio is smaller when it needs to recover, a phenomenon called sequence-of-returns risk. A deterministic projection that averages 7% every year misses this entirely, which is why a Monte Carlo simulation tests a retirement plan far better than one fixed average return does.

Box-Muller transform is the standard algorithm for generating normally-distributed random numbers from a uniform source:

Z = sqrt(-2 * ln(U1)) * cos(2 * pi * U2)
where U1, U2 are independent uniform random numbers on (0, 1)

The calculator uses 2,000 trials by default. Statistical power scales with the square root of trial count, so 2,000 trials gives a standard error of about ±1.1 percentage points on the success rate at 50%, accurate enough for planning decisions. The median ending balance (rather than mean) is reported because ending balances are heavily right-skewed: a few very successful paths pull the mean upward.

Worked examples

Example 1: Conservative retiree, 30-year horizon. Starting balance: R 1,000,000. Annual withdrawal: R 40,000. Years: 30. Expected return: 7%. Volatility: 15%. Running 2,000 simulations, this plan typically produces a success rate around 82-87%. The 4% withdrawal rule (R 40,000 / R 1,000,000) is the baseline, and 30 years is a long horizon that exposes the plan to more volatility, so a mid-80s success rate is normal.

Example 2: Aggressive retiree, 20-year horizon. Starting balance: R 800,000. Annual withdrawal: R 50,000. Years: 20. Expected return: 8%. Volatility: 18%. The higher withdrawal rate (6.25%) is offset by the shorter horizon. Success rates typically land around 75-82%. Above 90% would require either a higher starting balance or a lower withdrawal.

Example 3: Failing plan, diagnostic scenario. Starting balance: R 500,000. Annual withdrawal: R 50,000. Years: 30. Expected return: 6%. Volatility: 16%. This plan typically fails more than 40% of the time, because the withdrawal rate (10%) is well above what the portfolio can sustain. The output should prompt the user to either reduce withdrawals, work longer to grow the starting balance, or accept a much higher risk of outliving their savings.

Common mistakes

1. Treating the success rate as a probability of personal success. The simulation assumes your withdrawals, time horizon, and asset allocation are fixed for the entire retirement. In reality, most retirees adjust spending in response to market conditions, spending less after a bad year, more after a good one. A planner who uses flexible withdrawals typically achieves a higher real success rate than the model reports.

2. Using the wrong volatility assumption. Equity-heavy portfolios have a standard deviation around 15-18% for annual returns. A 60/40 stock/bond mix is closer to 10-12%. A 100% bond portfolio is around 5-7%. Using 15% volatility for a portfolio that's actually 100% bonds understates the real-world success rate.

3. Ignoring inflation in long horizons. Withdrawals are entered in today's dollars but the simulation does not index them to inflation. Over 30 years, a R 40,000 withdrawal that never increases has dramatically less purchasing power at the end than at the start. A more conservative analysis indexes withdrawals to inflation, which lowers the success rate.

4. Setting mean return too high. Long-run equity returns have averaged roughly 7% real (after inflation) historically. Using 10% or 12% "to be safe" produces inflated success rates. Use a return assumption you can defend with historical data, typically 6-8% real for diversified equity allocations.

5. Confusing median ending balance with expected value. The median ending balance is the midpoint of the distribution of outcomes. Half the paths end with more, half with less. A median of R 0 in a successful run does not mean the plan "almost failed", it means the typical successful trial left the retiree with about nothing at the end, which is fine if the goal was to spend the money, not leave an inheritance.

What Monte Carlo does and does not tell you

What it does well:

• Captures sequence-of-returns risk
• Gives a probability-style answer ("how often does this work?") that planners can act on
• Tests sensitivity to withdrawal rate, horizon, and asset allocation in one number
• Is fast and free to run, with no special software required

What it does not do:

• Model changing spending needs (healthcare, travel, family events)
• Account for taxes (capital gains, dividends, required minimum distributions)
• Model behavioral responses (reducing withdrawals after a bad year)
• Reflect non-normal return distributions (real markets have fatter tails)
• Replace personalized advice from a fee-only financial planner

Frequently Asked Questions

What is a "good" Monte Carlo success rate? The industry convention is 90% or higher for a comfortable plan, 80-90% for an acceptable plan with some risk of adjustment, and below 80% as a warning sign. Some planners use 85% as the threshold. The "right" number depends on your risk tolerance, your flexibility to adjust spending, and whether leaving an inheritance matters to you.

How many trials should I run? This calculator uses 2,000 trials, which gives an accuracy of roughly ±1 percentage point on the success rate. Statistical theory says standard error scales as 1/sqrt(N), so 10,000 trials would give ±0.5pp and 500 trials would give ±2pp. For most planning decisions, 1,000-2,000 trials is sufficient.

Why does the calculator use 7% as the default expected return? 7% real (after inflation) is close to the long-run historical average return for a diversified equity portfolio. It's a common planning default for retirement projections, though conservative planners may use 5-6% and aggressive planners may use 8-9%. Use a number that reflects your actual asset allocation, not a round-number default.

What is "standard deviation" of returns? Standard deviation measures how much returns vary year to year. A portfolio with 15% standard deviation will see roughly two-thirds of its annual returns fall within ±15% of the average, so a 7% average means most years are between -8% and +22%. A small standard deviation (under 5%) means stable, predictable returns (mostly bonds); a large one (over 20%) means wild swings (mostly small-cap stocks or emerging markets).

Does the simulation account for inflation? Not directly. Withdrawals are entered in today's dollars and not adjusted. To model inflation-adjusted withdrawals, increase the withdrawal amount to reflect expected inflation (e.g., 3% per year) over the retirement period. This is a conservative adjustment that will lower the success rate.

Is this calculator a substitute for a financial advisor? No. This is an educational tool. It uses a simplified model that doesn't capture taxes, changing spending needs, or behavioral responses. For retirement decisions involving more than a modest sum, consult a fee-only financial planner registered in your jurisdiction.

Why does my success rate change slightly between runs? The simulation uses random number generation, so each run is a different sample. With 2,000 trials, you should expect roughly ±1 percentage point of variation between runs. If you need a more precise number, the calculator could be extended to use more trials, at the cost of slower runs.

Related tools

• Retirement Calculator, deterministic projection of retirement savings
• Savings Calculator, how much you need to save to reach a goal
• Compound Interest Calculator, single-rate growth projection
• Investment Calculator, investment growth with periodic contributions
• Inflation Calculator, adjust dollar amounts for inflation
• ROI Calculator, return on investment for a single holding
• Budget Calculator, track monthly income and expenses
• Salary Calculator, convert between annual, monthly, and hourly pay

References

• Box, G. E. P.; Muller, M. E. (1958). "A Note on the Generation of Random Normal Deviates." Annals of Mathematical Statistics 29(2): 610-611.
• Pfau, Wade D. (2011). "Can We Predict the Sustainable Withdrawal Rate for Retirement?" Journal of Financial Planning.
• Bengen, William P. (1994). "Determining Withdrawal Rates Using Historical Data." Journal of Financial Planning 7(4): 171-180.
• Wikipedia: Monte Carlo method, Geometric Brownian motion, Sequence of returns risk.
• Investopedia: Monte Carlo Simulation, Safe Withdrawal Rate.

This calculator is for educational and planning purposes only. It is not financial advice, tax advice, or a recommendation to buy or sell any security. Consult a licensed financial advisor in your jurisdiction before making retirement planning decisions. Results depend on the accuracy of your inputs, particularly the expected return and volatility assumptions, and on the simplifying model assumptions described above.