function calculateEAR() {
// Get Input Values
var nominalRateInput = document.getElementById('nominalRateInput').value;
var periodsInput = document.getElementById('compoundingPeriodsInput').value;
var errorMsg = document.getElementById('errorMsg');
var resultBox = document.getElementById('resultBox');
// Validation
if (nominalRateInput === "" || isNaN(nominalRateInput) || nominalRateInput 0.05)
var i = r / 100;
// The Formula: EAR = (1 + i/n)^n – 1
var base = 1 + (i / n);
var earDecimal = Math.pow(base, n) – 1;
// Convert back to percentage
var earPercent = earDecimal * 100;
// Calculate the difference (Impact of compounding)
var difference = earPercent – r;
// Update UI
document.getElementById('resultEAR').innerHTML = earPercent.toFixed(4) + "%";
document.getElementById('resultNominal').innerHTML = r.toFixed(2) + "%";
document.getElementById('resultDiff').innerHTML = "+" + difference.toFixed(4) + "%";
document.getElementById('resultPeriods').innerHTML = n;
// Show Results
resultBox.style.display = 'block';
}
Understanding the Effective Annual Rate (EAR)
When comparing financial products, such as savings accounts, loans, or investments, the advertised interest rate—often called the "Nominal Rate"—rarely tells the whole story. The Effective Annual Rate (EAR), also known as the Annual Percentage Yield (APY), provides a more accurate measure of the actual return on an investment or the true cost of a loan.
The discrepancy between the nominal rate and the effective rate arises due to compounding. Compounding occurs when interest is paid on the principal amount plus any previously accumulated interest. The more frequently interest is compounded, the higher the effective rate will be compared to the nominal rate.
The Calculation Logic
The EAR formula converts a nominal interest rate that compounds more than once a year into a standard annual rate. This allows for an "apples-to-apples" comparison between financial products with different compounding schedules (e.g., monthly vs. quarterly).
EAR = (1 + r / n)n – 1
Where:
r represents the Nominal Annual Interest Rate (expressed as a decimal).
n represents the number of compounding periods per year.
Example Calculation
Imagine you have two investment options:
Option A: 5.00% interest compounded annually.
Option B: 4.90% interest compounded daily.
At a glance, Option A looks better. However, let's calculate the EAR for Option B:
Nominal Rate (r) = 0.049
Periods (n) = 365
Calculation: (1 + 0.049/365)365 – 1
Result: 5.02%
Surprisingly, the 4.90% rate compounded daily actually yields a higher return (5.02%) than the flat 5.00% compounded annually.
Why Compounding Frequency Matters
The frequency of compounding has a direct impact on the effective rate. As the number of compounding periods (n) increases, the EAR increases, though with diminishing returns.
Annual Compounding: EAR equals the Nominal Rate.
Semi-Annual to Monthly: Noticeable increase in EAR.
Daily Compounding: Highest standard discrete EAR.
This calculator helps investors maximize their savings by identifying true yields and helps borrowers understand the real cost of debt where interest capitalizes frequently, such as with credit cards.
Frequently Asked Questions
What is the difference between Nominal Rate and Effective Rate?
The nominal rate is the stated percentage interest rate usually quoted by banks (e.g., 5% per annum). The effective rate includes the effects of compounding within that year, showing what you actually earn or pay.
When should I use EAR?
Use EAR whenever you are comparing financial products with different compounding periods. For example, comparing a savings account that compounds monthly against a Certificate of Deposit (CD) that compounds quarterly.
Does this apply to loans?
Yes. In the context of lending, the EAR is often referred to as the Effective Annual Cost. It reveals that a loan with monthly compounding interest costs more than a loan with the same nominal rate but annual compounding.