Please check your inputs. The ending balance must be achievable.
Total Invested (Principal):
Total Profit/Gain:
Simple Return (Absolute):
Annualized Rate of Return:
How to Calculate Rate of Return with Contributions
Calculating investment performance becomes significantly more complex when you make regular contributions. Unlike a simple savings account where you deposit a lump sum and wait, most real-world portfolios involve ongoing investments—such as monthly deposits into a 401(k), IRA, or brokerage account. This calculator helps you determine your true Annualized Rate of Return (often comparable to the Money-Weighted Return or Internal Rate of Return) based on your starting balance, regular additions, and final portfolio value.
Why Simple Percentage Calculations Fail:
If you start with $10,000, add $5,000 halfway through the year, and end with $16,000, simply dividing your profit ($1,000) by your total contribution ($15,000) gives a misleading result. It ignores the fact that the initial $10,000 was invested for 12 months, while the $5,000 contribution was only invested for 6 months.
Understanding the Metrics
Starting Balance: The value of your portfolio at the beginning of the period.
Periodic Contribution: The amount of new money added to the portfolio on a regular schedule (e.g., monthly).
Ending Balance: The total value of your portfolio at the end of the time period.
Annualized Rate of Return: The calculated compound annual growth rate (CAGR) required to turn your starting balance and stream of contributions into the final ending balance.
The Mathematics Behind the Calculation
To accurately calculate the rate of return when contributions are involved, we use an iterative method to solve for the interest rate (r) in the Future Value of an Annuity formula equation. This is often referred to as the Money-Weighted Return.
The equation solved by this calculator is:
Final Value = [ P × (1 + r)^n ] + [ PMT × ( ((1 + r)^n – 1) / r ) ]
Where:
P = Starting Principal
PMT = Periodic Contribution
n = Total number of periods (e.g., months)
r = Rate of return per period
Because it is algebraically impossible to isolate r in this equation, the calculator uses a numerical method (bisection or Newton-Raphson) to find the rate that balances the equation exactly.
Example Calculation
Imagine you have an investment scenario:
Start: $10,000
Contribution: $500 per month
Duration: 5 years (60 months)
End Value: $55,000
Total Contributed: $10,000 + ($500 × 60) = $40,000. Total Profit: $55,000 – $40,000 = $15,000.
Using the calculator above, the Annualized Rate of Return would be approximately 11.45%. This means your money compounded at an effective annual rate of 11.45% to reach that final total.
When to Use This Calculator
Use this tool for:
Evaluating the performance of a mutual fund or stock portfolio where you practice "Dollar Cost Averaging."
Checking if your 401(k) growth is meeting your retirement planning assumptions.
Comparing real estate investments where you invest capital improvements over time.
function calculateRateOfReturn() {
// 1. Get Inputs
var startBal = parseFloat(document.getElementById("startBalance").value);
var contribution = parseFloat(document.getElementById("contributionAmount").value);
var freq = parseInt(document.getElementById("frequency").value);
var years = parseFloat(document.getElementById("years").value);
var endBal = parseFloat(document.getElementById("endBalance").value);
// UI Elements
var resultBox = document.getElementById("result");
var errorBox = document.getElementById("error");
// 2. Validate Inputs
if (isNaN(startBal) || isNaN(contribution) || isNaN(years) || isNaN(endBal) || years <= 0) {
resultBox.style.display = "none";
errorBox.style.display = "block";
errorBox.innerHTML = "Please enter valid numeric values for all fields.";
return;
}
// Logic Check: If End Balance is less than total contributions, return is negative.
// Total periods (n)
var n = years * freq;
// Total Cash Flow In
var totalInvested = startBal + (contribution * n);
// If inputs are valid, hide error
errorBox.style.display = "none";
// 3. Calculation: Iterative Solver for Rate (r)
// Formula: FV = PV * (1+r)^n + PMT * [ ( (1+r)^n – 1 ) / r ]
// We need to find 'r' (period rate)
// Edge case: No contributions
if (contribution === 0) {
if (startBal === 0) {
errorBox.style.display = "block";
errorBox.innerHTML = "Starting balance cannot be zero if there are no contributions.";
return;
}
// Simple CAGR formula: (End / Start)^(1/years) – 1
var cagr = Math.pow((endBal / startBal), (1 / years)) – 1;
displayResults(startBal, 0, endBal, cagr);
return;
}
// Bisection Method to find r
var low = -0.9999; // Lower bound (-100%)
var high = 10.0; // Upper bound (1000% per period – generous upper limit)
var epsilon = 0.0000001; // Precision
var guess = 0;
var iterations = 0;
var maxIterations = 1000;
var solvedRate = null;
while (iterations < maxIterations) {
guess = (low + high) / 2;
// Calculate FV using guess rate
// Avoid division by zero if guess is extremely close to 0
var fvCalc = 0;
if (Math.abs(guess) 0: FV = P + PMT*n
fvCalc = startBal + (contribution * n);
} else {
// Standard formula (assuming contributions made at END of period)
// FV = P*(1+r)^n + PMT * (((1+r)^n – 1) / r)
fvCalc = startBal * Math.pow(1 + guess, n) + contribution * ((Math.pow(1 + guess, n) – 1) / guess);
}
if (Math.abs(fvCalc – endBal) endBal) {
high = guess;
} else {
low = guess;
}
iterations++;
}
if (solvedRate === null) {
// Fallback if not converged (rare)
solvedRate = guess;
}
// Convert period rate to Annual Rate
// Annual Rate = (1 + r)^freq – 1
var annualRate = Math.pow(1 + solvedRate, freq) – 1;
// 4. Display Results
displayResults(startBal, contribution * n, endBal, annualRate);
}
function displayResults(start, totalContrib, end, annualRate) {
var totalInvested = start + totalContrib;
var profit = end – totalInvested;
var simpleReturn = 0;
if (totalInvested !== 0) {
simpleReturn = (profit / totalInvested) * 100;
}
// Formatting
var formatter = new Intl.NumberFormat('en-US', {
style: 'currency',
currency: 'USD',
minimumFractionDigits: 2
});
document.getElementById("resPrincipal").innerText = formatter.format(totalInvested);
document.getElementById("resProfit").innerText = formatter.format(profit);
// Color profit green or red
var profitEl = document.getElementById("resProfit");
if (profit >= 0) {
profitEl.style.color = "#27ae60";
} else {
profitEl.style.color = "#c0392b";
}
document.getElementById("resSimple").innerText = simpleReturn.toFixed(2) + "%";
document.getElementById("resAnnual").innerText = (annualRate * 100).toFixed(2) + "%";
document.getElementById("result").style.display = "block";
}