Equivalent Annual Rate Calculator

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Equivalent Annual Rate (EAR) Calculator .ear-calculator-container { max-width: 800px; margin: 0 auto; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif; color: #333; line-height: 1.6; } .ear-calc-box { background-color: #f8f9fa; border: 1px solid #e9ecef; border-radius: 8px; padding: 25px; margin-bottom: 40px; box-shadow: 0 4px 6px rgba(0,0,0,0.05); } .ear-input-group { margin-bottom: 20px; } .ear-input-label { display: block; margin-bottom: 8px; font-weight: 600; color: #2d3748; } .ear-input-field, .ear-select-field { width: 100%; padding: 12px; border: 1px solid #ced4da; border-radius: 4px; font-size: 16px; box-sizing: border-box; } .ear-input-field:focus, .ear-select-field:focus { border-color: #4a90e2; outline: none; box-shadow: 0 0 0 3px rgba(74, 144, 226, 0.2); } .ear-calc-btn { background-color: #0056b3; color: white; border: none; padding: 14px 20px; font-size: 16px; font-weight: 600; border-radius: 4px; cursor: pointer; width: 100%; transition: background-color 0.2s; } .ear-calc-btn:hover { background-color: #004494; } .ear-results-box { margin-top: 25px; background-color: #ffffff; border: 1px solid #dee2e6; border-radius: 6px; padding: 20px; display: none; } .ear-result-row { display: flex; justify-content: space-between; align-items: center; padding: 10px 0; border-bottom: 1px solid #f1f1f1; } .ear-result-row:last-child { border-bottom: none; } .ear-result-label { color: #495057; font-weight: 500; } .ear-result-value { font-weight: 700; font-size: 1.2em; color: #0056b3; } .ear-content-section h2 { color: #2c3e50; margin-top: 30px; border-bottom: 2px solid #eaeaea; padding-bottom: 10px; } .ear-content-section p { margin-bottom: 15px; text-align: justify; } .ear-content-section ul { margin-bottom: 20px; padding-left: 20px; } .ear-content-section li { margin-bottom: 8px; } .ear-formula-box { background-color: #eef2f7; padding: 15px; border-left: 4px solid #0056b3; font-family: "Courier New", Courier, monospace; margin: 20px 0; } .error-msg { color: #dc3545; font-size: 14px; margin-top: 5px; display: none; }

Equivalent Annual Rate Calculator

Please enter a valid positive number.
Annually (1 time/year) Semi-Annually (2 times/year) Quarterly (4 times/year) Monthly (12 times/year) Semi-Monthly (24 times/year) Bi-Weekly (26 times/year) Weekly (52 times/year) Daily (365 times/year)
Nominal Rate (Stated): 0.00%
Compounding Periods: 12
Equivalent Annual Rate (EAR): 0.00%
Effective Difference: +0.00%

What is Equivalent Annual Rate (EAR)?

The Equivalent Annual Rate (EAR), also known as the Effective Annual Rate (EFF), is a financial metric used to compare the interest rates of different financial products that have different compounding periods. While the nominal interest rate (or stated rate) tells you the percentage interest based on a year, it does not account for the effects of compounding within that year.

Compounding occurs when interest is added to the principal balance, and then the next period's interest is calculated on the new, higher balance. The more frequently interest is compounded, the higher the effective return (for savings) or cost (for loans) will be.

The EAR Formula

The calculation standardizes the rate to an annual period, allowing for an apples-to-apples comparison between a loan compounding monthly and an investment compounding quarterly. The formula is:

EAR = (1 + i/n)n – 1

Where:

  • i = The nominal (stated) annual interest rate (expressed as a decimal).
  • n = The number of compounding periods per year.

Why is EAR Important?

Understanding EAR is critical for making informed financial decisions:

  • For Investors: It reveals the true yield of an investment. A 5% nominal rate compounded daily yields more than a 5% nominal rate compounded annually.
  • For Borrowers: It reveals the true cost of debt. Credit cards, for example, often quote a nominal APR but compound daily, making the effective interest you pay significantly higher.

Calculation Example

Imagine you are comparing two savings accounts:

  1. Account A: Offers 6.0% interest compounded annually.
  2. Account B: Offers 5.9% interest compounded monthly.

Using the calculator:
Account A EAR: 6.0% (since n=1).
Account B EAR: (1 + 0.059/12)12 – 1 ≈ 6.06%.

Despite Account B having a lower nominal rate (5.9% vs 6.0%), it is actually the better option because the monthly compounding results in a higher effective annual yield.

Frequency Reference Table

Use the following values for "n" in manual calculations:

  • Annually: n = 1
  • Semi-Annually: n = 2
  • Quarterly: n = 4
  • Monthly: n = 12
  • Weekly: n = 52
  • Daily: n = 365
function calculateEAR() { // 1. Get DOM elements var nominalInput = document.getElementById('nominalRate'); var freqInput = document.getElementById('compoundingFreq'); var rateError = document.getElementById('rateError'); var resultsBox = document.getElementById('resultsDisplay'); // 2. Parse values var nominalRate = parseFloat(nominalInput.value); var n = parseInt(freqInput.value); // 3. Reset error state rateError.style.display = 'none'; nominalInput.style.borderColor = '#ced4da'; // 4. Validate Input if (isNaN(nominalRate) || nominalRate < 0) { rateError.style.display = 'block'; nominalInput.style.borderColor = '#dc3545'; resultsBox.style.display = 'none'; return; } // 5. Calculation Logic // Formula: EAR = (1 + r/n)^n – 1 // r must be decimal (e.g., 5% = 0.05) var r = nominalRate / 100; // Handle edge case where n is 0 or undefined (though select prevents this mostly) if (n = 0 ? "+" : ""; document.getElementById('diffRate').innerText = diffSign + diff.toFixed(3) + "%"; resultsBox.style.display = 'block'; }

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