function calculateCAGR() {
var initialInput = document.getElementById('initialInvestment');
var finalInput = document.getElementById('finalValue');
var yearsInput = document.getElementById('yearsHeld');
var resultsDiv = document.getElementById('resultsArea');
var errorDiv = document.getElementById('errorMsg');
// Reset display
resultsDiv.style.display = 'none';
errorDiv.style.display = 'none';
errorDiv.innerText = ";
var initial = parseFloat(initialInput.value);
var final = parseFloat(finalInput.value);
var years = parseFloat(yearsInput.value);
// Validation
if (isNaN(initial) || isNaN(final) || isNaN(years)) {
errorDiv.innerText = "Please enter valid numbers for all fields.";
errorDiv.style.display = 'block';
return;
}
if (initial <= 0) {
errorDiv.innerText = "Initial investment must be greater than zero to calculate a growth rate.";
errorDiv.style.display = 'block';
return;
}
if (years <= 0) {
errorDiv.innerText = "Number of years must be greater than zero.";
errorDiv.style.display = 'block';
return;
}
// Calculations
// 1. Total Gain: Final – Initial
var totalGain = final – initial;
// 2. Total Percentage Return: (Gain / Initial) * 100
var totalPercentReturn = (totalGain / initial) * 100;
// 3. CAGR Formula: (Final / Initial)^(1/Years) – 1
var ratio = final / initial;
// Handle negative final value mathematically for complex numbers?
// In finance, if final is negative, you lost more than 100%. CAGR doesn't handle negative bases well with fractional exponents.
// If Final is 0 or negative, CAGR represents a -100% loss effectively over the period or undefined in standard growth models.
var cagr = 0;
if (final < 0) {
// Edge case: complete loss situations are tricky in CAGR formula
errorDiv.innerText = "Final value cannot be negative for standard CAGR calculation.";
errorDiv.style.display = 'block';
return;
} else {
cagr = (Math.pow(ratio, (1 / years)) – 1) * 100;
}
// Formatting Output
document.getElementById('displayCAGR').innerText = cagr.toFixed(2) + "%";
document.getElementById('displayTotalGain').innerText = "$" + totalGain.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById('displayTotalPercent').innerText = totalPercentReturn.toFixed(2) + "%";
document.getElementById('displayYears').innerText = years;
// Show Results
resultsDiv.style.display = 'block';
}
How to Calculate Annual Rate of Return Over Multiple Years
Calculating your investment performance over a single year is straightforward, but measuring success over multiple years requires a more specific metric. When an investment spans several years, simply averaging the returns doesn't account for the effects of compounding. This is where the Compound Annual Growth Rate (CAGR) becomes essential.
This calculator determines the smoothed annual rate of growth of an investment over a specific time period defined by the user. It answers the question: "If my investment grew at a steady rate every single year to reach this final amount, what would that rate be?"
The Formula for Annual Rate of Return (CAGR)
The Annualized Rate of Return is calculated using the following mathematical formula:
CAGR = ( End Value / Start Value ) ^ ( 1 / n ) – 1
Where:
End Value is the final value of the investment or portfolio.
Start Value is the initial principal invested.
n is the number of years the investment was held.
Example Calculation
Let's say you purchased stock worth $10,000. After 5 years, you sold that stock for $15,000. How do you calculate the annual return?
Determine the Ratio: Divide the final value by the initial value ($15,000 / $10,000 = 1.5).
Apply the Time Exponent: Raise this ratio to the power of one divided by the number of years (1 / 5 = 0.2). So, 1.5 ^ 0.2 ≈ 1.08447.
Subtract One: 1.08447 – 1 = 0.08447.
Convert to Percentage: Multiply by 100 to get 8.45%.
This means your investment grew at an effective annual rate of 8.45% over those 5 years.
Why Not Use Simple Average Return?
A simple average can be misleading because it ignores compounding. In the example above, the total return was 50% over 5 years. A simple average would suggest 10% per year (50% / 5). However, the true Annualized Return (CAGR) is 8.45%. The simple average overestimates your return because it doesn't account for the fact that gains in early years generate their own gains in later years.
Key Considerations
Time Period: The formula works for any time period, but "n" must be expressed in years. If you invested for 18 months, "n" would be 1.5.
Volatility: CAGR smoothes out volatility. It implies a steady growth rate, even if the actual investment value fluctuated wildly up and down during the holding period.
Contributions: This basic CAGR calculation assumes a lump sum investment at the start with no additional contributions or withdrawals during the period. For calculating returns with regular deposits, an Internal Rate of Return (XIRR) calculator would be more appropriate.