function calculateEffectiveRate() {
// Get Inputs
var nominalInput = document.getElementById('nominalRate').value;
var frequencyInput = document.getElementById('compoundingFreq').value;
var resultBox = document.getElementById('resultBox');
// Basic Validation
if (nominalInput === "" || isNaN(nominalInput)) {
alert("Please enter a valid nominal interest rate.");
return;
}
var r = parseFloat(nominalInput); // Nominal rate in percent
var r_decimal = r / 100; // Nominal rate as decimal
var ear = 0;
var periodic = 0;
var diff = 0;
// Logic
if (frequencyInput === 'continuous') {
// Formula: e^r – 1
ear = (Math.exp(r_decimal) – 1);
periodic = 0; // Not applicable really, but mathematically it's the limit
} else {
// Formula: (1 + r/n)^n – 1
var n = parseInt(frequencyInput);
var base = 1 + (r_decimal / n);
ear = Math.pow(base, n) – 1;
periodic = (r / n);
}
// Convert EAR back to percentage
var earPercent = ear * 100;
diff = earPercent – r;
// Display Results
document.getElementById('effectiveRateResult').innerHTML = earPercent.toFixed(4) + "%";
document.getElementById('nominalRateDisplay').innerHTML = r.toFixed(2) + "%";
var diffSign = diff >= 0 ? "+" : "";
document.getElementById('rateDifference').innerHTML = diffSign + diff.toFixed(4) + "%";
if (frequencyInput === 'continuous') {
document.getElementById('periodicRate').innerHTML = "N/A (Continuous)";
} else {
document.getElementById('periodicRate').innerHTML = periodic.toFixed(4) + "%";
}
// Show box
resultBox.style.display = "block";
}
Understanding the Effective Rate Calculation Formula
In finance and economics, the difference between the "sticker price" of an interest rate and what you actually earn (or pay) can be significant. This discrepancy is resolved by using the Effective Annual Rate (EAR), also known as the Annual Percentage Yield (APY).
What is the Effective Annual Rate?
The Nominal Interest Rate is the simple percentage rate stated for a year (like 5% per annum). However, it does not account for the effects of intra-year compounding. If an investment pays interest monthly, the interest earned in January starts earning its own interest in February. This "interest on interest" effect means the actual yield at the end of the year is higher than the nominal rate.
The Effective Rate Calculation Formula converts a nominal rate into an annualized rate that includes the impact of compounding, allowing for an apples-to-apples comparison between financial products with different compounding schedules.
The Calculation Formula
The standard formula for calculating the effective rate depends on the compounding frequency ($n$):
EAR = (1 + r/n)n – 1
Where:
EAR = Effective Annual Rate (as a decimal)
r = Nominal Annual Interest Rate (as a decimal)
n = Number of compounding periods per year
Continuous Compounding
In theoretical finance or specific banking products, compounding might happen continuously. The formula changes to use Euler's number ($e$):
At first glance, Option A looks better (12% vs 11.5%). However, let's calculate the Effective Rate for Option B:
r = 0.115, n = 12
EAR = (1 + 0.115/12)12 – 1 = 12.12%
Because of monthly compounding, Option B actually yields a higher return (12.12%) than Option A (12.00%), despite having a lower nominal rate. This illustrates why understanding the effective rate calculation formula is crucial for maximizing returns on savings or minimizing costs on loans.
Common Compounding Frequencies
When using this calculator, select the 'n' value that matches your financial product:
Annually (n=1): Common for simple bonds.
Semi-Annually (n=2): Standard for US Treasury bonds.
Quarterly (n=4): Common for stock dividends.
Monthly (n=12): Standard for savings accounts, mortgages, and credit cards.
Daily (n=365): Often used for high-yield savings accounts or commercial loans.