Formula to Calculate Annual Rate of Return

Annual Rate of Return Calculator .arr-calculator-container { max-width: 800px; margin: 0 auto; font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background: #ffffff; border-radius: 8px; box-shadow: 0 4px 15px rgba(0,0,0,0.1); padding: 20px; } .arr-header { text-align: center; background-color: #2c3e50; color: white; padding: 15px; border-radius: 8px 8px 0 0; margin: -20px -20px 20px -20px; } .arr-header h2 { margin: 0; font-size: 1.5rem; } .arr-form-group { margin-bottom: 20px; } .arr-form-group label { display: block; margin-bottom: 8px; font-weight: 600; color: #34495e; } .arr-input-wrapper { position: relative; } .arr-input-wrapper input { width: 100%; padding: 12px; border: 1px solid #ddd; border-radius: 4px; font-size: 16px; box-sizing: border-box; transition: border-color 0.3s; } .arr-input-wrapper input:focus { border-color: #3498db; outline: none; } .arr-btn { width: 100%; padding: 14px; background-color: #27ae60; color: white; border: none; border-radius: 4px; font-size: 18px; font-weight: bold; cursor: pointer; transition: background-color 0.3s; } .arr-btn:hover { background-color: #219150; } #arr-result { margin-top: 25px; padding: 20px; background-color: #f8f9fa; border-left: 5px solid #27ae60; border-radius: 4px; display: none; } .arr-result-item { display: flex; justify-content: space-between; margin-bottom: 10px; padding-bottom: 10px; border-bottom: 1px solid #eee; } .arr-result-item:last-child { border-bottom: none; margin-bottom: 0; padding-bottom: 0; } .arr-result-label { color: #7f8c8d; font-weight: 500; } .arr-result-value { font-weight: 700; color: #2c3e50; font-size: 1.1rem; } .arr-highlight { color: #27ae60; font-size: 1.4rem; } .arr-content { margin-top: 40px; line-height: 1.6; color: #333; } .arr-content h3 { color: #2c3e50; border-bottom: 2px solid #ecf0f1; padding-bottom: 10px; margin-top: 30px; } .formula-box { background-color: #f1f8ff; padding: 15px; border-radius: 5px; font-family: 'Courier New', Courier, monospace; text-align: center; margin: 20px 0; border: 1px solid #d0e1f5; } @media (max-width: 600px) { .arr-result-item { flex-direction: column; align-items: flex-start; } .arr-result-value { margin-top: 5px; } }

Annual Rate of Return Calculator

Enter decimal for partial years (e.g., 2.5 years)

How to Calculate Annual Rate of Return

The Annual Rate of Return (often referred to as the Annualized Return or CAGR – Compound Annual Growth Rate) provides a geometric mean return that represents the consistent annual growth rate required for an investment to grow from its beginning balance to its ending balance over a specific time period.

Unlike a simple percentage return, which only looks at the total profit relative to the investment, the annual rate of return accounts for the time factor. This makes it a crucial metric for comparing investments held for different lengths of time.

The Annual Return Formula

To calculate the annual rate of return manually, you can use the following formula:

Annual Return = ((Ending Value / Beginning Value) ^ (1 / Years)) – 1

Where:

  • Ending Value: The current value of the investment or the value at the time of sale.
  • Beginning Value: The initial amount invested.
  • Years: The holding period expressed in years.

Real-World Example

Let's say you invested $10,000 in a mutual fund.

  • After 3 years, your investment is worth $14,500.
  • Total Return: ($14,500 – $10,000) / $10,000 = 45%.
  • Annual Rate of Return: To find the annual compounding rate:

Calculation: (14,500 / 10,000)^(1 / 3) – 1
= (1.45)^(0.3333) – 1
= 1.1318 – 1
= 13.18%

This means your investment grew at an effective rate of 13.18% every year to reach the final amount.

Why It Matters

Using the annual rate of return is superior to simple return when analyzing long-term investments. A 50% total return sounds impressive, but if it took 20 years to achieve, the annual return is only about 2%. Conversely, a 50% return over 2 years represents a stellar 22.47% annual return.

function calculateReturn() { // Get input elements by ID strictly matching HTML var startInput = document.getElementById('beginningValue'); var endInput = document.getElementById('endingValue'); var yearsInput = document.getElementById('holdingPeriod'); var resultDiv = document.getElementById('arr-result'); // Parse values var startVal = parseFloat(startInput.value); var endVal = parseFloat(endInput.value); var years = parseFloat(yearsInput.value); // Validation if (isNaN(startVal) || isNaN(endVal) || isNaN(years)) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Please enter valid numbers in all fields.'; return; } if (startVal <= 0) { resultDiv.style.display = 'block'; resultDiv.innerHTML = 'Beginning Value must be greater than zero.'; return; } if (years = 0 ? '#27ae60' : '#c0392b'; // Construct Result HTML var html = "; html += '
'; html += 'Annual Rate of Return (CAGR):'; html += '' + annualReturnPct.toFixed(2) + '%'; html += '
'; html += '
'; html += 'Total Percentage Return:'; html += '' + totalReturnPct.toFixed(2) + '%'; html += '
'; html += '
'; html += 'Total Profit / Loss:'; html += '$' + totalProfit.toLocaleString('en-US', {minimumFractionDigits: 2, maximumFractionDigits: 2}) + ''; html += '
'; // Display results resultDiv.style.display = 'block'; resultDiv.innerHTML = html; }

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