Retirement Monte Carlo Simulation Calculator
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Retirement Monte Carlo Simulation Calculator
Simulation Results
Enter your details and run the simulation.
Understanding the Retirement Monte Carlo Simulation
A Monte Carlo simulation for retirement planning is a powerful tool that uses randomness to model a wide range of potential financial outcomes for your retirement savings. Instead of relying on a single, fixed projection, it runs thousands of different scenarios, each based on slightly varied assumptions about investment returns, inflation, and other factors. This gives you a more realistic picture of the probabilities of achieving your retirement goals.
How it Works:
The core idea is to simulate the future based on probabilities. Here's a simplified breakdown of the process:
- Input Your Data: You provide key information such as your current age, desired retirement age, current savings, planned annual contributions, expected average annual investment return, average annual inflation rate, and your desired annual income in retirement.
- Simulate Investment Returns: For each simulation run, the calculator generates a random annual investment return for each year until and during retirement. These returns are not fixed; they are drawn from a statistical distribution (often a normal distribution) based on your *expected average annual return* and a measure of volatility (standard deviation). The greater the expected return and volatility, the wider the range of possible outcomes.
- Account for Inflation: Each year's expenses (especially desired retirement income) are adjusted for inflation, which also varies randomly within a plausible range around your expected inflation rate.
- Track Savings Growth: Your current savings grow (or shrink) based on the simulated investment returns and your annual contributions, while also being depleted by your living expenses, all adjusted for inflation.
- Run Thousands of Times: This entire process is repeated for a large number of simulations (e.g., 1,000 or 10,000).
- Analyze Outcomes: The results are then aggregated. You can see the probability that your savings will last throughout retirement, the average outcome, the range of potential outcomes (e.g., the 10th percentile to the 90th percentile), and how likely you are to meet or exceed your desired retirement income.
Key Metrics:
- Probability of Success: The percentage of simulations where your savings lasted for your expected lifespan in retirement.
- Median Outcome: The result that occurred in 50% of the simulations (a good representation of a typical outcome).
- Range of Outcomes: Often presented as percentiles (e.g., 10th to 90th), showing the spread between the worst and best plausible scenarios.
Why Use Monte Carlo?
Traditional retirement calculators often use a single, linear projection. This can be misleading because real-world investment returns fluctuate significantly year to year. Monte Carlo simulations acknowledge this uncertainty, providing a more robust and realistic assessment of your retirement readiness. It helps you understand your risk tolerance and make informed decisions about saving, investing, and retirement planning.
Example Calculation Logic (Simplified):
For each year (let's say year 't') within a single simulation:
- Calculate Real Return:
real_return_t = (1 + expected_return_t) / (1 + inflation_t) - 1
- Calculate Savings at Year End:
savings_t = savings_{t-1} * (1 + real_return_t) + contributions_t
- Calculate Income Needed (if in retirement):
income_needed_t = desired_income * (1 + inflation)^t
- Update Savings (if in retirement):
savings_t = savings_{t-1} - income_needed_t
The calculator repeats these steps for thousands of iterations, varying `expected_return_t` and `inflation_t` based on statistical distributions.
function runMonteCarloSimulation() {
// Get input values
var currentAge = parseInt(document.getElementById("currentAge").value);
var retirementAge = parseInt(document.getElementById("retirementAge").value);
var currentSavings = parseFloat(document.getElementById("currentSavings").value);
var annualContributions = parseFloat(document.getElementById("annualContributions").value);
var expectedAnnualReturn = parseFloat(document.getElementById("expectedAnnualReturn").value) / 100; // Convert to decimal
var annualInflation = parseFloat(document.getElementById("annualInflation").value) / 100; // Convert to decimal
var desiredRetirementIncome = parseFloat(document.getElementById("desiredRetirementIncome").value);
var numSimulations = parseInt(document.getElementById("monteCarloSimulations").value);
var resultsDiv = document.getElementById("results");
resultsDiv.innerHTML = 'Running simulations…';
// Basic input validation
if (isNaN(currentAge) || isNaN(retirementAge) || isNaN(currentSavings) || isNaN(annualContributions) ||
isNaN(expectedAnnualReturn) || isNaN(annualInflation) || isNaN(desiredRetirementIncome) || isNaN(numSimulations)) {
resultsDiv.innerHTML = 'Please enter valid numbers for all fields.';
return;
}
if (currentAge >= retirementAge) {
resultsDiv.innerHTML = 'Desired Retirement Age must be greater than Current Age.';
return;
}
if (expectedAnnualReturn 0.3) { // Realistic bounds for expected return
resultsDiv.innerHTML = 'Expected Annual Return seems unrealistic. Please check.';
return;
}
if (annualInflation 0.15) { // Realistic bounds for inflation
resultsDiv.innerHTML = 'Annual Inflation seems unrealistic. Please check.';
return;
}
var retirementYears = retirementAge – currentAge;
var totalSimulationsRun = 0;
var successfulSimulations = 0;
var finalSavingsAtRetirement = []; // Store ending balance at retirement age for each simulation
var durationOfRetirement = []; // Store how long savings last in retirement
// Define volatility (standard deviation) – a common assumption for stock market is ~15-20%
var volatility = 0.18; // Example: 18% standard deviation
// Function to generate a random number from a normal distribution (Box-Muller transform)
function randomNormal() {
var u = 0, v = 0;
while(u === 0) u = Math.random(); //Converting [0,1) to (0,1)
while(v === 0) v = Math.random();
return Math.sqrt( -2.0 * Math.log( u ) ) * Math.cos( 2.0 * Math.PI * v );
}
for (var i = 0; i < numSimulations; i++) {
var currentBalance = currentSavings;
var currentAgeInSim = currentAge;
var contributionsThisYear = annualContributions;
var simulationSuccessful = true;
var yearsRetired = 0;
var inflationFactorCurrent = Math.pow(1 + annualInflation, currentAge – currentAge); // Inflation from start to current age
// Accumulate savings until retirement
while (currentAgeInSim < retirementAge) {
var randomReturn = randomNormal() * volatility;
var actualAnnualReturn = expectedAnnualReturn + randomReturn;
// Ensure returns are not absurdly negative or positive in a single year
if (actualAnnualReturn 1.0) actualAnnualReturn = 1.0; // Cap positive returns at 100%
// Calculate real return considering inflation
var realReturn = (1 + actualAnnualReturn) / (1 + annualInflation) – 1;
currentBalance = currentBalance * (1 + realReturn) + contributionsThisYear;
// Ensure balance doesn't go below zero due to extreme negative returns + withdrawals
if (currentBalance = 0) { // Continue as long as there's money
// Adjust income needed for inflation from the year of retirement
var currentYearInflationFactor = Math.pow(1 + annualInflation, yearsRetired);
var adjustedIncomeNeeded = desiredRetirementIncome * currentYearInflationFactor;
if (currentBalance >= adjustedIncomeNeeded) {
currentBalance -= adjustedIncomeNeeded;
yearsRetired++;
} else {
// Ran out of money this year
simulationSuccessful = false;
break;
}
// Optional: Cap retirement duration for very long simulations
if (yearsRetired > 100) { // e.g., max 100 years in retirement
simulationSuccessful = true; // Assume success if they have money for 100 years
break;
}
}
if (simulationSuccessful) {
successfulSimulations++;
durationOfRetirement.push(yearsRetired);
}
totalSimulationsRun++;
}
// Calculate results
var successProbability = (successfulSimulations / numSimulations) * 100;
var avgFinalSavings = 0;
if (finalSavingsAtRetirement.length > 0) {
for (var j = 0; j 0) {
for (var k = 0; k 0 ? durationOfRetirement[Math.floor(durationOfRetirement.length * 0.1)] : 0;
var p90Duration = durationOfRetirement.length > 0 ? durationOfRetirement[Math.floor(durationOfRetirement.length * 0.9)] : 0;
// Format numbers for display
function formatCurrency(amount) {
if (isNaN(amount) || amount === null) return "N/A";
return '$' + amount.toFixed(0).replace(/\B(?=(\d{3})+(?!\d))/g, ",");
}
function formatYears(years) {
if (isNaN(years) || years === null || years === 0) return "N/A";
return years.toFixed(0) + " Years";
}
resultsDiv.innerHTML = `
Success Probability: ${successProbability.toFixed(1)}%
Average Final Savings at Retirement: ${formatCurrency(avgFinalSavings)}
10th Percentile Final Savings: ${formatCurrency(p10Savings)} (Worst 10% of outcomes)
90th Percentile Final Savings: ${formatCurrency(p90Savings)} (Best 10% of outcomes)
Average Retirement Duration: ${formatYears(avgRetirementDuration)}
10th Percentile Duration: ${formatYears(p10Duration)}
90th Percentile Duration: ${formatYears(p90Duration)}
`;
}