Retirement Calculator Monte Carlo

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Retirement Monte Carlo Simulator

Use this calculator to estimate the probability of your retirement savings lasting through your desired retirement period, considering market volatility and inflation.











Results:

Probability of Success:

Median Portfolio at Life Expectancy:

Worst-Case (5th Percentile) Portfolio:

Best-Case (95th Percentile) Portfolio:

Understanding the Monte Carlo Retirement Simulator

Traditional retirement calculators often use a single, fixed rate of return to project your future savings. While simple, this approach fails to account for the inherent unpredictability of financial markets. The Monte Carlo Retirement Simulator addresses this by running thousands of different scenarios, each with varying market returns and inflation rates, to give you a more realistic picture of your retirement prospects.

How it Works:

The simulator takes your current financial situation and retirement goals, then projects your portfolio's growth and withdrawals year by year. For each year in each simulation, it randomly generates a market return based on your specified expected return and volatility. During retirement, it also adjusts your desired income for inflation. By repeating this process many times, it can determine the probability that your savings will last throughout your retirement.

Key Inputs Explained:

  • Current Age: Your current age in years.
  • Desired Retirement Age: The age at which you plan to stop working and begin drawing from your retirement savings.
  • Life Expectancy: The age you expect to live to. This defines the duration of your retirement withdrawal phase.
  • Current Retirement Savings ($): The total amount you currently have saved for retirement.
  • Annual Savings Contribution ($): The amount you plan to save each year until retirement.
  • Desired Annual Retirement Income ($): The annual income you wish to have in retirement (in today's dollars).
  • Expected Annual Return (%): Your anticipated average annual return on investments. This is a long-term average.
  • Expected Annual Volatility (%): The standard deviation of your expected annual returns. Higher volatility means greater swings in market performance.
  • Expected Annual Inflation (%): The average rate at which the cost of living is expected to increase.
  • Number of Simulations: The more simulations, the more accurate the probability estimate, but also the longer the calculation. 1,000 to 10,000 is usually sufficient.

Interpreting the Results:

  • Probability of Success: This is the most crucial metric. It tells you the percentage of simulations where your portfolio did NOT run out of money before your life expectancy. A higher percentage (e.g., 80% or more) generally indicates a more robust plan.
  • Median Portfolio at Life Expectancy: The middle value of all simulated portfolio balances at your life expectancy. Half of the simulations resulted in a portfolio balance above this amount, and half below.
  • Worst-Case (5th Percentile) Portfolio: This shows the portfolio balance at your life expectancy in the bottom 5% of simulations. It represents a scenario where market conditions were particularly unfavorable.
  • Best-Case (95th Percentile) Portfolio: This shows the portfolio balance at your life expectancy in the top 5% of simulations. It represents a scenario where market conditions were particularly favorable.

Example Scenario:

Let's say a 30-year-old has $100,000 in savings, plans to save $10,000 annually, and wants to retire at 65 with $50,000 annual income, expecting to live until 90. With an expected annual return of 7%, volatility of 15%, and inflation of 3%, running 1,000 simulations might yield:

  • Probability of Success: 78%
  • Median Portfolio at Life Expectancy: $1,250,000
  • Worst-Case (5th Percentile) Portfolio: -$150,000 (meaning the money ran out)
  • Best-Case (95th Percentile) Portfolio: $3,500,000

This example suggests a reasonable chance of success, but also highlights the risk of running out of money in less favorable market conditions. Adjusting inputs like increasing savings, delaying retirement, or reducing desired income can improve the success rate.

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} .calculator-results { margin-top: 30px; padding-top: 20px; border-top: 1px solid #e0e0e0; } .calculator-results p { margin-bottom: 10px; font-size: 17px; color: #34495e; } .calculator-results span { font-weight: bold; color: #007bff; } .calculator-article { margin-top: 30px; padding-top: 20px; border-top: 1px solid #e0e0e0; color: #555; line-height: 1.6; } .calculator-article h4 { color: #2c3e50; margin-top: 20px; margin-bottom: 10px; } .calculator-article ul { list-style-type: disc; margin-left: 20px; margin-bottom: 15px; } .calculator-article li { margin-bottom: 5px; } // Helper function to generate a random number from a normal distribution (Box-Muller transform) function getRandomNormal(mean, stdDev) { var u = 0, v = 0; while (u === 0) u = Math.random(); // Converting [0,1) to (0,1) while (v === 0) v = Math.random(); var z = Math.sqrt(-2.0 * Math.log(u)) * Math.cos(2.0 * Math.PI * v); return z * stdDev + mean; } // Helper function to get a percentile from a sorted array function getPercentile(arr, p) { if (arr.length === 0) return 0; arr.sort(function(a, b) { return a – b; }); // Ensure array is sorted var index = (p / 100) * (arr.length – 1); var lower = Math.floor(index); var upper = Math.ceil(index); var weight = index – lower; if (lower === upper) return arr[lower]; return arr[lower] * (1 – weight) + arr[upper] * weight; } function calculateMonteCarlo() { var currentAge = parseFloat(document.getElementById("currentAge").value); var retirementAge = parseFloat(document.getElementById("retirementAge").value); var lifeExpectancy = parseFloat(document.getElementById("lifeExpectancy").value); var currentSavings = parseFloat(document.getElementById("currentSavings").value); var annualSavings = parseFloat(document.getElementById("annualSavings").value); var desiredIncome = parseFloat(document.getElementById("desiredIncome").value); var expectedReturn = parseFloat(document.getElementById("expectedReturn").value) / 100; // Convert to decimal var expectedVolatility = parseFloat(document.getElementById("expectedVolatility").value) / 100; // Convert to decimal var expectedInflation = parseFloat(document.getElementById("expectedInflation").value) / 100; // Convert to decimal var numSimulations = parseInt(document.getElementById("numSimulations").value); var errorMessageDiv = document.getElementById("errorMessage"); errorMessageDiv.innerHTML = ""; // Clear previous errors // Input validation if (isNaN(currentAge) || isNaN(retirementAge) || isNaN(lifeExpectancy) || isNaN(currentSavings) || isNaN(annualSavings) || isNaN(desiredIncome) || isNaN(expectedReturn) || isNaN(expectedVolatility) || isNaN(expectedInflation) || isNaN(numSimulations)) { errorMessageDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (currentAge <= 0 || retirementAge <= 0 || lifeExpectancy <= 0 || numSimulations <= 0) { errorMessageDiv.innerHTML = "Age, life expectancy, and number of simulations must be positive."; return; } if (retirementAge <= currentAge) { errorMessageDiv.innerHTML = "Retirement Age must be greater than Current Age."; return; } if (lifeExpectancy <= retirementAge) { errorMessageDiv.innerHTML = "Life Expectancy must be greater than Retirement Age."; return; } if (currentSavings < 0 || annualSavings < 0 || desiredIncome < 0) { errorMessageDiv.innerHTML = "Savings and desired income values cannot be negative."; return; } if (expectedVolatility < 0) { errorMessageDiv.innerHTML = "Expected Volatility cannot be negative."; return; } var finalPortfolioValues = []; var successfulSimulations = 0; for (var i = 0; i < numSimulations; i++) { var portfolio = currentSavings; var currentDesiredIncome = desiredIncome; var ranOutOfMoney = false; // Accumulation Phase for (var year = currentAge; year < retirementAge; year++) { var annualReturn = getRandomNormal(expectedReturn, expectedVolatility); portfolio = portfolio * (1 + annualReturn); portfolio += annualSavings; } // Withdrawal Phase for (var year = retirementAge; year < lifeExpectancy; year++) { var annualReturn = getRandomNormal(expectedReturn, expectedVolatility); // Adjust desired income for inflation for the current year's withdrawal currentDesiredIncome = currentDesiredIncome * (1 + expectedInflation); portfolio = portfolio * (1 + annualReturn); portfolio -= currentDesiredIncome; if (portfolio <= 0) { ranOutOfMoney = true; break; // Portfolio ran out, this simulation failed } } if (!ranOutOfMoney) { successfulSimulations++; finalPortfolioValues.push(portfolio); } else { finalPortfolioValues.push(0); // Mark as 0 if it ran out } } var successRate = (successfulSimulations / numSimulations) * 100; var medianPortfolio = getPercentile(finalPortfolioValues, 50); var worstCasePortfolio = getPercentile(finalPortfolioValues, 5); var bestCasePortfolio = getPercentile(finalPortfolioValues, 95); document.getElementById("successRate").innerHTML = successRate.toFixed(2) + "%"; document.getElementById("medianPortfolio").innerHTML = "$" + medianPortfolio.toLocaleString(undefined, {minimumFractionDigits: 0, maximumFractionDigits: 0}); document.getElementById("worstCasePortfolio").innerHTML = "$" + worstCasePortfolio.toLocaleString(undefined, {minimumFractionDigits: 0, maximumFractionDigits: 0}); document.getElementById("bestCasePortfolio").innerHTML = "$" + bestCasePortfolio.toLocaleString(undefined, {minimumFractionDigits: 0, maximumFractionDigits: 0}); }

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