The Effective Annual Rate (EAR), also known as the Annual Equivalent Rate (AER) or sometimes the 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 a nominal interest rate is the stated rate, the EAR reflects the actual percentage increase in value over a year due to interest being added to the principal multiple times.
When interest is compounded more than once a year (e.g., monthly, quarterly, or semi-annually), the EAR will be higher than the nominal interest rate. This is because interest earned in earlier periods starts earning interest itself in subsequent periods. The EAR is crucial for comparing different financial products, especially those with varying compounding frequencies. A higher EAR means you earn more on your investments or pay more on your loans, all else being equal.
How to Calculate EAR
The formula used to calculate the EAR is:
EAR = (1 + (r/n))^n – 1
Where:
r is the nominal annual interest rate (expressed as a decimal). In this calculator, this is represented by the 'Periodic Interest Rate' multiplied by the 'Number of Compounding Periods per Year'. For the purpose of this calculator, we directly input the periodic rate.
n is the number of compounding periods per year.
This calculator simplifies the input by asking for the periodic interest rate directly and the number of compounding periods per year.
Example Calculation:
Let's say you have an investment with a nominal annual interest rate of 12% that compounds monthly.
The periodic interest rate (r/n) would be 12% / 12 = 1% or 0.01 as a decimal.
The number of compounding periods per year (n) is 12 (monthly).
Using the formula:
EAR = (1 + 0.01)^12 – 1
EAR = (1.01)^12 – 1
EAR = 1.126825 – 1
EAR = 0.126825
This translates to an EAR of approximately 12.68%.
function calculateEAR() {
var periodicRateInput = document.getElementById("periodicRate");
var periodsPerYearInput = document.getElementById("periodsPerYear");
var resultDiv = document.getElementById("result");
var periodicRate = parseFloat(periodicRateInput.value);
var periodsPerYear = parseInt(periodsPerYearInput.value);
// Validate inputs
if (isNaN(periodicRate) || isNaN(periodsPerYear) || periodicRate < 0 || periodsPerYear <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for the periodic rate and periods per year.";
return;
}
// EAR = (1 + periodicRate)^periodsPerYear – 1
var effectiveAnnualRate = Math.pow(1 + periodicRate, periodsPerYear) – 1;
// Format the result as a percentage
var formattedEAR = (effectiveAnnualRate * 100).toFixed(4);
resultDiv.innerHTML = "