function calculateEffectiveRate() {
// 1. Get DOM elements
var rateInput = document.getElementById('nominalRateInput');
var freqInput = document.getElementById('compoundingSelect');
var resultBox = document.getElementById('resultContainer');
var resultValue = document.getElementById('earResultValue');
var resultDetail = document.getElementById('earDifference');
// 2. Parse values
var nominalRatePercent = parseFloat(rateInput.value);
var compoundingFreq = parseInt(freqInput.value);
// 3. Validation
if (isNaN(nominalRatePercent) || nominalRatePercent < 0) {
alert("Please enter a valid positive nominal interest rate.");
return;
}
// 4. Logic: EAR = (1 + r/n)^n – 1
// Convert percentage to decimal
var r = nominalRatePercent / 100;
var n = compoundingFreq;
// Calculation
var base = 1 + (r / n);
var earDecimal = Math.pow(base, n) – 1;
// Convert back to percentage
var earPercent = earDecimal * 100;
// Calculate difference
var difference = earPercent – nominalRatePercent;
// 5. Display Result
resultBox.style.display = 'block';
resultValue.innerHTML = earPercent.toFixed(4) + '%';
resultDetail.innerHTML = "This rate is " + difference.toFixed(4) + "% higher than your nominal rate due to compounding.";
}
Understanding the Effective Annual Rate Formula
When comparing financial products—whether they are loans, savings accounts, or investment opportunities—the "headline" interest rate often doesn't tell the whole story. This is where the Effective Annual Rate (EAR) becomes a crucial metric. The EAR calculator above helps you convert a nominal interest rate into the true effective rate, accounting for the frequency of compounding.
What is Effective Annual Rate (EAR)?
The Effective Annual Rate (also known as the Annual Equivalent Rate or AER) represents the actual interest rate earned or paid on an investment or loan over the course of a year. Unlike the nominal rate, the EAR takes into account the effects of compounding periods.
Compounding occurs when interest is added to the principal balance, and then that added interest earns even more interest. The more frequently interest is compounded, the higher the effective rate will be compared to the nominal rate.
The EAR Formula
To calculate the effective annual rate manually, financial analysts use the following mathematical formula:
EAR = (1 + i/n)n – 1
Where:
EAR = Effective Annual Rate
i = Nominal Annual Interest Rate (expressed as a decimal)
Result: The EAR for Account B is approximately 10.25%. Even though the nominal rate is lower, the monthly compounding makes Account B the more profitable choice.
Why Compounding Frequency Matters
The frequency of compounding has a direct impact on the outcome of your investment or the cost of your debt. Common compounding periods include:
Monthly (n=12): Common for credit cards, mortgages, and savings accounts.
Quarterly (n=4): Often seen in stock dividends or business loans.
Daily (n=365): Used for some high-yield savings accounts and credit card interest calculations.
As 'n' increases, the gap between the nominal rate and the effective rate widens. This calculator allows you to instantly visualize that gap to make better financial decisions.
Nominal vs. Effective Rate
The Nominal Rate is the stated interest rate without adjusting for compounding. It is the rate often advertised because it looks lower for loans or simpler for basic comparisons.
The Effective Rate is the rate you actually pay or earn. It provides a standard "apples-to-apples" comparison regardless of how different the compounding schedules are between two financial products.