Calculating Compound Annual Growth Rate

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Compound Annual Growth Rate (CAGR) Calculator

function calculateCAGR() { var initialValue = parseFloat(document.getElementById("initialValue").value); var finalValue = parseFloat(document.getElementById("finalValue").value); var numberOfYears = parseFloat(document.getElementById("numberOfYears").value); var resultDiv = document.getElementById("result"); if (isNaN(initialValue) || isNaN(finalValue) || isNaN(numberOfYears) || initialValue <= 0 || numberOfYears <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for all fields."; return; } // CAGR formula: ((Ending Value / Starting Value)^(1 / Number of Years)) – 1 var cagr = Math.pow((finalValue / initialValue), (1 / numberOfYears)) – 1; // Format the result as a percentage var formattedCAGR = (cagr * 100).toFixed(2) + "%"; resultDiv.innerHTML = "

Result:

The Compound Annual Growth Rate (CAGR) is: " + formattedCAGR + ""; } .calculator-container { font-family: sans-serif; max-width: 600px; margin: 20px auto; padding: 20px; border: 1px solid #ccc; border-radius: 8px; box-shadow: 0 2px 4px rgba(0, 0, 0, 0.1); } .calculator-container h2 { text-align: center; margin-bottom: 20px; color: #333; } .input-section { display: grid; grid-template-columns: 1fr; gap: 15px; } .form-group { display: flex; flex-direction: column; } .form-group label { margin-bottom: 5px; font-weight: bold; color: #555; } .form-group input { padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 16px; } button { background-color: #4CAF50; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; transition: background-color 0.3s ease; margin-top: 10px; } button:hover { background-color: #45a049; } .result-section { margin-top: 25px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 4px; color: #155724; } .result-section h3 { margin-top: 0; color: #155724; }

Understanding Compound Annual Growth Rate (CAGR)

The Compound Annual Growth Rate (CAGR) is a vital metric used to measure the average annual growth of an investment or a business metric over a specified period, assuming that the profits were reinvested at the end of each year.

Why CAGR is Important

CAGR provides a smoothed rate of return, making it easier to understand the performance of an investment over time. It's particularly useful for comparing the performance of different investments or for projecting future growth based on historical data. Unlike simple average growth rates, CAGR accounts for the effect of compounding, where growth in one period builds upon the growth from previous periods.

How CAGR is Calculated

The formula for calculating CAGR is:

CAGR = ((Ending Value / Starting Value)^(1 / Number of Years)) - 1

Let's break down the formula:

  • Ending Value: The value of the investment or metric at the end of the period.
  • Starting Value: The value of the investment or metric at the beginning of the period.
  • Number of Years: The total number of years over which the growth is measured.

The result of this formula is a decimal, which is then typically multiplied by 100 to express it as a percentage.

Example Calculation

Imagine an investment started with a value of $10,000 and grew to $25,000 over a period of 5 years. To calculate the CAGR:

  • Starting Value = $10,000
  • Ending Value = $25,000
  • Number of Years = 5

Using the formula:

CAGR = (($25,000 / $10,000)^(1 / 5)) - 1

CAGR = (2.5^(0.2)) - 1

CAGR = 1.2011 - 1

CAGR = 0.2011

As a percentage, the CAGR is approximately 20.11%.

When to Use CAGR

CAGR is widely used by:

  • Investors: To assess the historical performance of stocks, mutual funds, or portfolios.
  • Businesses: To track revenue growth, profit growth, customer acquisition rates, or market share expansion over time.
  • Analysts: To compare the growth trajectories of different companies or industries.

It's important to remember that CAGR represents a hypothetical smoothed rate. Actual year-over-year growth can be much more volatile.

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