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 effect of compounding interest. Unlike the nominal annual interest rate, which does not account for compounding within the year, the EAR provides a more accurate picture of the true cost of borrowing or the true yield of an investment over a one-year period.
The EAR is particularly important when comparing different financial products that may have different compounding frequencies. For instance, an account compounding monthly will have a higher EAR than an account with the same nominal rate compounding annually.
EAR Calculation Formula:
The formula to calculate the Effective Annual Rate (EAR) is:
EAR = (1 + r/n)^n – 1
Where:
EAR is the Effective Annual Rate.
r is the nominal annual interest rate (expressed as a decimal).
n is the number of compounding periods per year.
How to Use the EAR Calculator:
To use this calculator, simply input the following:
Nominal Annual Interest Rate (%): Enter the stated annual interest rate (e.g., 5 for 5%).
Number of Compounding Periods per Year: Indicate how many times the interest is compounded within a year (e.g., 1 for annually, 2 for semi-annually, 4 for quarterly, 12 for monthly, 365 for daily).
Click the "Calculate EAR" button, and the calculator will display the effective annual rate, also expressed as a percentage.
Example Calculation:
Let's say you have an investment with a nominal annual interest rate of 6% that compounds monthly.
Nominal Annual Interest Rate (r) = 6% or 0.06
Number of Compounding Periods per Year (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
Therefore, the Effective Annual Rate (EAR) is approximately 6.17%.
function calculateEAR() {
var nominalRateInput = document.getElementById("nominalRate").value;
var compoundingPeriodsInput = document.getElementById("compoundingPeriods").value;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (nominalRateInput === "" || compoundingPeriodsInput === "") {
resultDiv.innerHTML = "Please enter values for both fields.";
return;
}
var nominalRate = parseFloat(nominalRateInput);
var compoundingPeriods = parseInt(compoundingPeriodsInput, 10);
if (isNaN(nominalRate) || isNaN(compoundingPeriods) || compoundingPeriods <= 0) {
resultDiv.innerHTML = "Please enter valid numbers for the inputs. Compounding periods must be a positive integer.";
return;
}
var ratePerPeriod = nominalRate / 100 / compoundingPeriods;
var ear = Math.pow((1 + ratePerPeriod), compoundingPeriods) – 1;
if (isNaN(ear)) {
resultDiv.innerHTML = "Calculation error. Please check your inputs.";
} else {
resultDiv.innerHTML = "