The Effective Annual Rate (EAR), also known as the Annual Percentage Yield (APY) in banking contexts, is a crucial metric for investors and borrowers alike. It represents the actual annual return on an investment or the true annualized cost of a loan when the effects of compounding are taken into account.
While the Nominal Interest Rate is the stated percentage rate, it does not account for how often interest is calculated and added back to the principal. The EAR provides a normalized way to compare financial products with different compounding periods.
Why EAR Matters
Financial institutions often advertise the nominal rate because it looks lower for borrowers and simple to understand. However, the frequency of compounding can significantly alter the actual amount paid or earned. As the frequency of compounding increases, the effective rate becomes higher than the nominal rate.
For Savers: A higher EAR means your money grows faster. You want to maximize this number.
For Borrowers: A higher EAR means you are paying more in interest. You want to minimize this number.
The EAR Formula
The calculation uses the nominal rate and the number of compounding periods per year. The formula is:
EAR = (1 + i / n)n – 1
Where:
i = The nominal annual interest rate (expressed as a decimal).
n = The number of compounding periods per year (e.g., 12 for monthly, 365 for daily).
Real-World Example
Let's say you are comparing two savings accounts:
Account A: Offers a 5.0% nominal rate compounded annually.
Account B: Offers a 4.9% nominal rate compounded daily.
At first glance, Account A looks better. However, let's calculate the EAR:
Account A: (1 + 0.05 / 1)^1 – 1 = 5.00%
Account B: (1 + 0.049 / 365)^365 – 1 ≈ 5.02%
Despite the lower nominal rate, Account B actually yields a higher return due to the power of daily compounding.
Compounding Frequencies
Common compounding periods used in finance include:
Daily (n=365): Common for savings accounts and credit cards.
Monthly (n=12): Standard for mortgages, car loans, and some savings accounts.
Quarterly (n=4): Often used for dividend payments and corporate bonds.
Semi-Annually (n=2): Typical for treasury bonds.
function calculateEAR() {
// Get input values
var nominalInput = document.getElementById('nominalRate').value;
var frequencyInput = document.getElementById('compoundingFreq').value;
// Validate inputs
if (nominalInput === "" || nominalInput === null) {
alert("Please enter a Nominal Annual Interest Rate.");
return;
}
// Parse values
var nominalRate = parseFloat(nominalInput);
var n = parseInt(frequencyInput);
// Edge case validation
if (isNaN(nominalRate) || nominalRate 0) {
diffResult.innerHTML = "Compounding adds " + difference.toFixed(4) + "% to the nominal rate.";
} else {
diffResult.innerHTML = "With annual compounding, the effective rate equals the nominal rate.";
}
}