:root {
–primary-color: #2c3e50;
–secondary-color: #27ae60;
–accent-color: #ecf0f1;
–text-color: #34495e;
–border-radius: 8px;
}
body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: var(–text-color);
max-width: 800px;
margin: 0 auto;
padding: 20px;
background-color: #f9f9f9;
}
.calculator-container {
background: white;
padding: 30px;
border-radius: var(–border-radius);
box-shadow: 0 4px 6px rgba(0,0,0,0.1);
margin-bottom: 40px;
border-top: 5px solid var(–secondary-color);
}
h1 {
text-align: center;
color: var(–primary-color);
margin-bottom: 20px;
}
.input-group {
margin-bottom: 20px;
}
label {
display: block;
margin-bottom: 8px;
font-weight: 600;
color: var(–primary-color);
}
input[type="number"] {
width: 100%;
padding: 12px;
border: 1px solid #ddd;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
transition: border-color 0.3s;
}
input[type="number"]:focus {
border-color: var(–secondary-color);
outline: none;
}
.hint {
font-size: 0.85em;
color: #7f8c8d;
margin-top: 5px;
}
button {
width: 100%;
padding: 15px;
background-color: var(–secondary-color);
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.3s;
}
button:hover {
background-color: #219150;
}
#results {
margin-top: 25px;
padding: 20px;
background-color: var(–accent-color);
border-radius: var(–border-radius);
display: none;
border-left: 4px solid var(–secondary-color);
}
.result-row {
display: flex;
justify-content: space-between;
align-items: center;
margin-bottom: 10px;
font-size: 1.1em;
}
.result-row.highlight {
font-size: 1.5em;
font-weight: bold;
color: var(–secondary-color);
border-top: 1px solid #bdc3c7;
padding-top: 10px;
margin-top: 10px;
}
.content-section {
background: white;
padding: 30px;
border-radius: var(–border-radius);
box-shadow: 0 2px 4px rgba(0,0,0,0.05);
}
h2 {
color: var(–primary-color);
border-bottom: 2px solid var(–accent-color);
padding-bottom: 10px;
margin-top: 30px;
}
.formula-box {
background-color: #f8f9fa;
border: 1px solid #e9ecef;
padding: 15px;
text-align: center;
font-family: "Courier New", monospace;
font-weight: bold;
margin: 20px 0;
border-radius: 4px;
}
.example-box {
background-color: #e8f6f3;
padding: 15px;
border-left: 4px solid var(–secondary-color);
margin: 15px 0;
}
ul {
padding-left: 20px;
}
li {
margin-bottom: 10px;
}
How is Compound Annual Growth Rate Calculated?
The Compound Annual Growth Rate (CAGR) is one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time. Unlike an average annual return, CAGR assumes that the profits are reinvested at the end of each period of the investment's lifespan.
Investors specifically use CAGR to measure and compare the past performance of investments or to project their expected future returns. It smoothes out the volatility of periodic returns and provides a single geometric mean representing the constant rate at which the investment would have grown if it had grown at a steady rate.
The CAGR Formula
To understand how CAGR is calculated, you must look at the mathematical relationship between the beginning value, the ending value, and the time elapsed. The formula is:
CAGR = (Ending Value / Beginning Value)(1 / n) – 1
Where:
- Ending Value: The value of the investment at the end of the period.
- Beginning Value: The value of the investment at the start of the period.
- n: The number of years (or periods) involved.
Step-by-Step Calculation Guide
Follow these steps to perform the calculation manually:
- Divide the Ending Value by the Beginning Value to find the total growth multiple.
- Raise the result to the power of one divided by the number of years (1/n). This is equivalent to taking the nth root.
- Subtract 1 from the result.
- Multiply by 100 to convert the decimal into a percentage.
Real-World Example
Scenario: You invested $10,000 in a mutual fund.
- Year 1 Value: $10,000 (Start)
- Year 5 Value: $19,500 (End)
- Time Period: 5 Years
Calculation:
1. Divide End by Start: 19,500 / 10,000 = 1.95
2. Exponent calculation: 1.95(1/5) = 1.950.2 = 1.1428
3. Subtract 1: 1.1428 – 1 = 0.1428
4. Convert to Percentage: 14.28%
Result: The CAGR is 14.28%. This means the investment grew as if it had compounded at a steady 14.28% annually.
Why is CAGR Important?
CAGR is superior to "average annual return" because it accounts for the effects of compounding. For example, if an investment loses 50% in the first year and gains 50% in the second year, the average return is 0%, but you have actually lost money (starting at $100, going to $50, then to $75). The CAGR would accurately reflect this negative performance.
However, it is important to remember that CAGR is a smoothed figure. It describes the rate at which an investment would have grown if it had grown at a steady rate, which rarely happens in reality. It does not reflect the investment risk or volatility that occurred during the time period.
function calculateCAGR() {
// Get input values using var
var startVal = document.getElementById('startValue').value;
var endVal = document.getElementById('endValue').value;
var years = document.getElementById('periodYears').value;
// Parse values to floats
var start = parseFloat(startVal);
var end = parseFloat(endVal);
var n = parseFloat(years);
// Validation Logic
if (isNaN(start) || isNaN(end) || isNaN(n)) {
alert("Please enter valid numbers for all fields.");
return;
}
if (start <= 0) {
alert("Beginning Value must be greater than 0.");
return;
}
if (n = 0) {
document.getElementById('cagrResult').style.color = '#27ae60'; // Green
} else {
document.getElementById('cagrResult').style.color = '#c0392b'; // Red
}
}