3.3 Interest Rate Calculator

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Compound Annual Growth Rate (CAGR) Calculator

.calculator-container { font-family: sans-serif; max-width: 600px; margin: 20px auto; padding: 20px; border: 1px solid #ccc; border-radius: 8px; background-color: #f9f9f9; } .calculator-inputs { display: grid; grid-template-columns: repeat(auto-fit, minmax(200px, 1fr)); gap: 15px; margin-bottom: 20px; } .input-group { display: flex; flex-direction: column; } .input-group label { margin-bottom: 5px; font-weight: bold; color: #333; } .input-group input[type="number"] { padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 16px; } .calculator-container button { padding: 12px 20px; background-color: #007bff; color: white; border: none; border-radius: 4px; font-size: 16px; cursor: pointer; transition: background-color 0.3s ease; width: fit-content; margin-top: 10px; } .calculator-container button:hover { background-color: #0056b3; } .calculator-result { margin-top: 20px; padding: 15px; background-color: #e9ecef; border: 1px solid #ced4da; border-radius: 4px; font-size: 18px; font-weight: bold; color: #212529; text-align: center; } function calculateCAGR() { var startValue = parseFloat(document.getElementById("startValue").value); var endValue = parseFloat(document.getElementById("endValue").value); var numberOfYears = parseFloat(document.getElementById("numberOfYears").value); var resultElement = document.getElementById("result"); if (isNaN(startValue) || isNaN(endValue) || isNaN(numberOfYears) || startValue <= 0 || numberOfYears <= 0) { resultElement.innerHTML = "Please enter valid positive numbers for all fields."; return; } if (endValue < 0) { resultElement.innerHTML = "Ending value cannot be negative."; return; } var cagr = Math.pow((endValue / startValue), (1 / numberOfYears)) – 1; var percentageCAGR = (cagr * 100).toFixed(2) + "%"; resultElement.innerHTML = "Compound Annual Growth Rate (CAGR): " + percentageCAGR; }

Understanding Compound Annual Growth Rate (CAGR)

The Compound Annual Growth Rate (CAGR) is a vital metric used to measure the average annual rate of return of an investment over a specified period longer than one year. It represents the smoothed-out annual growth rate, assuming that profits were reinvested at the end of each year of the investment's lifespan. CAGR is particularly useful because it helps to normalize volatility, providing a single figure that represents the growth trajectory of an investment.

Why is CAGR Important?

  • Simplifies Growth Measurement: It cuts through the noise of year-to-year fluctuations, offering a clear picture of long-term performance.
  • Comparison Tool: CAGR allows investors to easily compare the performance of different investments with varying growth patterns over the same time frame.
  • Forecasting: While not a predictor of future results, CAGR can be used as a basis for estimating potential future values of an investment.
  • Business Performance: Companies use CAGR to assess the growth of revenue, profits, or other key performance indicators over time.

How is CAGR Calculated?

The formula for CAGR is:

CAGR = ( (Ending Value / Beginning Value) ^ (1 / Number of Years) ) - 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.
  • Number of Years: The total duration of the investment period in years.

The result is typically expressed as a percentage.

Example:

Let's say you invested $10,000 in a stock (Starting Value). After 5 years (Number of Years), your investment has grown to $25,000 (Ending Value).

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

Using the CAGR calculator above or the formula:

CAGR = ( ($25,000 / $10,000) ^ (1 / 5) ) - 1
CAGR = ( 2.5 ^ 0.2 ) - 1
CAGR = 1.2011 - 1
CAGR = 0.2011

Expressed as a percentage, the CAGR is approximately 20.11%. This means your investment grew at an average rate of 20.11% per year over the 5-year period, smoothing out any daily or monthly fluctuations.

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