Calculate the Effective Annual Rate

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Effective Annual Rate (EAR) Calculator

What is the Effective Annual Rate (EAR)?

The Effective Annual Rate (EAR), also known as the Annual Equivalent Rate (AER) or effective interest rate, is the real rate of return earned on an investment or paid on a loan, taking into account the effects of compounding interest. While the nominal interest rate is the stated rate, the EAR reflects the actual interest earned or paid over a year when interest is compounded more than once per year.

Why is EAR Important?

  • Comparison: EAR allows for a fair comparison between financial products that have different compounding frequencies. For instance, a savings account with a 5% nominal annual rate compounded monthly will yield a higher EAR than an account with the same nominal rate compounded quarterly.
  • Real Return: It provides a more accurate picture of the true cost of borrowing or the true return on savings.
  • Decision Making: Understanding EAR helps in making informed financial decisions, whether you are choosing an investment, a loan, or a savings account.

How to Calculate EAR

The formula for calculating the Effective Annual Rate is:

EAR = (1 + (Nominal Rate / n))^n – 1

Where:

  • Nominal Rate: This is the stated annual interest rate, expressed as a decimal.
  • n: This is the number of compounding periods per year.

The result is usually expressed as a percentage by multiplying by 100.

Example Calculation

Let's say you have an investment with a nominal annual rate of 6% (0.06) that compounds monthly (n=12).

  • Nominal Rate = 6% or 0.06
  • Compounding Periods (n) = 12 (for monthly compounding)

Using the formula:

EAR = (1 + (0.06 / 12))^12 – 1

EAR = (1 + 0.005)^12 – 1

EAR = (1.005)^12 – 1

EAR = 1.0616778 – 1

EAR = 0.0616778

As a percentage, the EAR is approximately 6.17%.

function calculateEAR() { var nominalRateInput = document.getElementById("nominalRate").value; var compoundingPeriodsInput = document.getElementById("compoundingPeriods").value; var resultDiv = document.getElementById("result"); // Clear previous results resultDiv.innerHTML = ""; // Validate inputs if (nominalRateInput === "" || compoundingPeriodsInput === "") { resultDiv.innerHTML = "Please enter both values."; return; } var nominalRate = parseFloat(nominalRateInput); var compoundingPeriods = parseFloat(compoundingPeriodsInput); if (isNaN(nominalRate) || isNaN(compoundingPeriods)) { resultDiv.innerHTML = "Please enter valid numbers for both fields."; return; } if (compoundingPeriods <= 0) { resultDiv.innerHTML = "Number of compounding periods per year must be greater than zero."; return; } if (nominalRate < 0) { resultDiv.innerHTML = "Nominal rate cannot be negative for this calculation."; return; } // Convert nominal rate from percentage to decimal if it's entered as a whole number percentage (e.g., 5 for 5%) // This assumes user enters '5' for 5%, not '0.05' var rateAsDecimal = nominalRate / 100; // Calculate EAR var ear = Math.pow((1 + (rateAsDecimal / compoundingPeriods)), compoundingPeriods) – 1; // Format and display the result var formattedEAR = (ear * 100).toFixed(2); resultDiv.innerHTML = "The Effective Annual Rate (EAR) is: " + formattedEAR + "%"; }

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