In finance, interest rates can be deceptive depending on how often they are compounded. An "Equivalent Rate" refers to the conversion of an interest rate compounded at one frequency (e.g., monthly) to a rate compounded at a different frequency (e.g., annually) that produces the exact same amount of interest over the same period.
Nominal vs. Effective Rates
The Nominal Rate is the stated annual interest rate without taking compounding into account. For example, a 12% nominal rate compounded monthly actually results in more interest than a 12% nominal rate compounded annually.
The Effective Annual Rate (EAR), also known as the Annual Equivalent Rate (AER), represents the true return on an investment or the true cost of a loan when compounding is factored in.
Why Use This Calculator?
Comparing financial products can be difficult when lenders or banks quote rates with different compounding periods. One bank might offer 5% compounded quarterly, while another offers 4.9% compounded daily. To compare them fairly, you must convert them to an equivalent basis (usually the Effective Annual Rate).
The Formulas Used
This calculator uses the standard financial conversion formulas:
Where r is the nominal rate, n is the current compounding frequency per year, and m is the target frequency.
Example Calculation
If you have a nominal rate of 10% compounded Monthly (12 times a year), the Effective Annual Rate (EAR) is approximately 10.47%. This means your money grows by 10.47% in a year, not just 10%.
function calculateEquivalentRates() {
// Get Inputs
var rateInput = document.getElementById('nominal_rate');
var freqFromInput = document.getElementById('current_freq');
var freqToInput = document.getElementById('target_freq');
var errorMsg = document.getElementById('rate_error');
var resultsPanel = document.getElementById('results_panel');
// Parse Values
var nominalRate = parseFloat(rateInput.value);
var freqFrom = parseInt(freqFromInput.value);
var freqTo = parseInt(freqToInput.value);
// Validation
if (isNaN(nominalRate) || nominalRate < 0) {
errorMsg.style.display = 'block';
resultsPanel.style.display = 'none';
return;
} else {
errorMsg.style.display = 'none';
}
var ear = 0;
var targetRate = 0;
var decimalRate = nominalRate / 100;
// 1. Calculate Effective Annual Rate (EAR)
// Handle Continuous Compounding (Frequency = 0)
if (freqFrom === 0) {
// Formula: e^r – 1
ear = Math.exp(decimalRate) – 1;
} else {
// Formula: (1 + r/n)^n – 1
ear = Math.pow((1 + (decimalRate / freqFrom)), freqFrom) – 1;
}
// 2. Calculate Target Equivalent Rate from EAR
if (freqTo === 0) {
// Convert EAR to Continuous: ln(1 + EAR)
targetRate = Math.log(1 + ear);
} else {
// Convert EAR to Discrete: m * ((1 + EAR)^(1/m) – 1)
targetRate = freqTo * (Math.pow((1 + ear), (1 / freqTo)) – 1);
}
// 3. Calculate Periodic Rate (Rate per compounding period)
var periodicRate = 0;
if (freqTo !== 0) {
periodicRate = targetRate / freqTo;
}
// Convert back to percentages
var earPercent = ear * 100;
var targetRatePercent = targetRate * 100;
var periodicRatePercent = periodicRate * 100;
// Display Results
document.getElementById('result_ear').innerHTML = earPercent.toFixed(4) + '%';
var targetLabel = "";
var freqText = freqToInput.options[freqToInput.selectedIndex].text;
// Clean up text for label display (remove the n/year part)
freqText = freqText.split('(')[0].trim();
if (freqTo === 0) {
document.getElementById('result_target_rate').innerHTML = targetRatePercent.toFixed(4) + '% (Continuous)';
document.getElementById('result_periodic').innerHTML = "N/A (Continuous)";
} else {
document.getElementById('result_target_rate').innerHTML = targetRatePercent.toFixed(4) + '% (' + freqText + ')';
document.getElementById('result_periodic').innerHTML = periodicRatePercent.toFixed(4) + '%';
}
// Show panel
resultsPanel.style.display = 'block';
}
function resetEquivalentCalc() {
document.getElementById('nominal_rate').value = '';
document.getElementById('current_freq').value = '12';
document.getElementById('target_freq').value = '1';
document.getElementById('results_panel').style.display = 'none';
document.getElementById('rate_error').style.display = 'none';
}