.ear-calculator-container {
max-width: 600px;
margin: 20px auto;
padding: 20px;
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
font-family: Arial, sans-serif;
box-shadow: 0 2px 5px rgba(0,0,0,0.05);
}
.ear-calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.ear-form-group {
margin-bottom: 15px;
}
.ear-form-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.ear-form-group input, .ear-form-group select {
width: 100%;
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
.ear-btn {
width: 100%;
padding: 12px;
background-color: #28a745;
color: white;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
font-weight: bold;
margin-top: 10px;
}
.ear-btn:hover {
background-color: #218838;
}
.ear-result {
margin-top: 20px;
padding: 15px;
background-color: #fff;
border: 1px solid #e2e6ea;
border-radius: 4px;
text-align: center;
font-size: 18px;
color: #333;
}
.ear-result strong {
font-size: 24px;
color: #28a745;
display: block;
margin-top: 10px;
}
.ear-article {
max-width: 800px;
margin: 40px auto;
font-family: Arial, sans-serif;
line-height: 1.6;
color: #333;
}
.ear-article h2 {
margin-top: 30px;
color: #2c3e50;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
}
.ear-article h3 {
color: #34495e;
margin-top: 20px;
}
.ear-article p {
margin-bottom: 15px;
}
.ear-article ul {
margin-bottom: 15px;
padding-left: 20px;
}
.ear-article code {
background-color: #f4f4f4;
padding: 2px 5px;
border-radius: 3px;
font-family: monospace;
color: #c7254e;
}
.excel-box {
background-color: #e8f5e9;
border-left: 5px solid #28a745;
padding: 15px;
margin: 20px 0;
}
function calculateEffectiveRate() {
var nominalStr = document.getElementById('nominalRate').value;
var periodsStr = document.getElementById('compoundingFreq').value;
var resultDiv = document.getElementById('earResult');
// Reset display
resultDiv.style.display = 'block';
if (nominalStr === "" || periodsStr === "") {
resultDiv.innerHTML = "Please enter both the Nominal Rate and select a Compounding Frequency.";
resultDiv.style.color = "#dc3545";
return;
}
var r = parseFloat(nominalStr);
var n = parseFloat(periodsStr);
// Validation logic
if (isNaN(r) || isNaN(n) || n <= 0) {
resultDiv.innerHTML = "Please enter valid numeric values.";
resultDiv.style.color = "#dc3545";
return;
}
// Calculation: EAR = (1 + r/n)^n – 1
// Note: r input is percentage, so divide by 100 first
var rDecimal = r / 100;
var earDecimal = Math.pow((1 + (rDecimal / n)), n) – 1;
var earPercent = earDecimal * 100;
// Formatting result
var finalResult = earPercent.toFixed(4); // 4 decimal places for precision
resultDiv.style.color = "#333";
resultDiv.innerHTML = "Effective Annual Rate (EAR):
Understanding the Effective Annual Rate (EAR) Calculator
When evaluating investment returns or loan costs, the "nominal" percentage rate often tells an incomplete story. The Effective Annual Rate (EAR), also known as the Annual Equivalent Rate (AER), provides a true representation of financial growth or cost by accounting for the effects of compounding periods within a single year.
This calculator functions similarly to the effective annual rate calculator features found in Microsoft Excel, allowing you to instantly convert a nominal rate into an effective rate based on compounding frequency.
The Mathematics of Compounding
The discrepancy between a nominal rate and an effective rate arises from compounding—the process where interest is earned on previously earned interest. If compounding happens more than once a year (e.g., monthly or daily), the actual yield will be higher than the stated nominal rate.
The mathematical formula used in this calculator is:
EAR = (1 + i/n)n – 1
Where:
- i = The nominal annual rate (expressed as a decimal).
- n = The number of compounding periods per year.
How to Calculate Effective Annual Rate in Excel
Many financial professionals use Excel to perform this calculation. If you are building a spreadsheet, you do not need to manually enter the complex formula above. Excel provides a built-in function specifically for this purpose.
Excel Syntax
Formula: =EFFECT(nominal_rate, npery)
Parameters:
nominal_rate: The nominal interest rate (e.g., 0.10 for 10%).npery: The number of compounding periods per year (e.g., 12 for monthly).
Example Calculation
Let's say you are looking at a savings account offering a 5% nominal rate, but it compounds monthly. What is your actual return?
- Nominal Rate (i): 0.05
- Periods (n): 12
- Calculation: (1 + 0.05/12)12 – 1
- Result: 0.05116… or 5.116%
In Excel, you would simply type: =EFFECT(5%, 12) to get the same result. The calculator above performs this exact logic instantly without requiring spreadsheet software.
Why Use EAR?
Comparing financial products with different compounding schedules can be misleading if you only look at the nominal rate. A loan with a lower nominal rate compounded daily might actually be more expensive than a loan with a slightly higher nominal rate that compounds annually. The Effective Annual Rate standardizes these figures, providing a clear "apples-to-apples" comparison metric.
Common Compounding Frequencies
When inputting the "Compounding Periods per Year" into the calculator or Excel, use the following standard values:
- Annually: 1
- Semi-Annually: 2
- Quarterly: 4
- Monthly: 12
- Weekly: 52
- Daily: 365 (or sometimes 360 in commercial finance)