Annually (Once a year)
Semi-Annually (Twice a year)
Quarterly (4 times a year)
Monthly (12 times a year)
Weekly (52 times a year)
Daily (365 times a year)
Please enter a valid interest rate greater than 0.
Annual Equivalent Rate (AER)
0.00%
How to Calculate Annual Equivalent Rate (AER)
The Annual Equivalent Rate (AER) is a crucial financial metric used to standardize interest rates for savings accounts and investments. Unlike the nominal (or gross) interest rate, the AER accounts for the effects of compound interest. It illustrates what the interest rate would be if interest was paid and compounded exactly once per year.
Understanding AER allows savers to compare financial products fairly, even if they have different compounding frequencies (e.g., monthly vs. annually).
The AER Formula
To calculate the AER manually, you need two variables: the nominal interest rate ($r$) and the number of compounding periods per year ($n$).
AER = (1 + r/n)n – 1
r: The stated annual nominal interest rate (as a decimal).
n: The number of times interest is paid/compounded per year.
Step-by-Step Calculation Guide
Convert the Rate: Divide your percentage rate by 100 to get a decimal. (e.g., 5% becomes 0.05).
Determine Frequency: Identify how many times per year interest is paid.
Monthly = 12
Quarterly = 4
Daily = 365
Divide: Divide the decimal rate ($r$) by the frequency ($n$).
Add One: Add 1 to the result from step 3.
Exponentiate: Raise the result of step 4 to the power of the frequency ($n$).
Subtract One: Subtract 1 from the result.
Convert to Percentage: Multiply by 100 to get the AER percentage.
Real-World Example
Imagine you have a savings account offering a 5% nominal rate, but interest is paid monthly.
Using the logic above:
$r = 0.05$
$n = 12$
Calculation: $(1 + 0.05/12)^{12} – 1$
Inside parenthesis: $1 + 0.0041666… = 1.0041666…$
Power of 12: $(1.0041666…)^{12} \approx 1.05116$
Subtract 1: $0.05116$
AER: 5.12%
Because the interest is compounded monthly, your effective return (AER) is slightly higher than the stated 5%.
Why is AER Higher than the Gross Rate?
AER is typically higher than the gross nominal rate because of the "interest on interest" effect. When interest is paid monthly, the interest earned in January starts earning its own interest in February. By the end of the year, this compounding effect results in a higher total return compared to a simple annual payment.
Compounding Frequency
Nominal Rate
Calculated AER
Annually
5.00%
5.00%
Semi-Annually
5.00%
5.06%
Quarterly
5.00%
5.09%
Monthly
5.00%
5.12%
Daily
5.00%
5.13%
When to Use This Calculator
Use this tool when comparing savings accounts, certificates of deposit (CDs), or investment bonds where the provider pays interest at different intervals. It ensures you are comparing "apples to apples" to find the best return on your money.
function calculateAER() {
// 1. Get input values
var nominalRateInput = document.getElementById('nominalRate').value;
var freqInput = document.getElementById('compoundingFreq').value;
var errorMsg = document.getElementById('errorMsg');
var resultSection = document.getElementById('resultSection');
// 2. Parse values
var r_percent = parseFloat(nominalRateInput);
var n = parseInt(freqInput);
// 3. Validation
if (isNaN(r_percent) || r_percent < 0 || nominalRateInput === "") {
errorMsg.style.display = "block";
resultSection.style.display = "none";
return;
} else {
errorMsg.style.display = "none";
}
// 4. Calculation Logic: AER = (1 + r/n)^n – 1
// Convert percentage to decimal
var r_decimal = r_percent / 100;
// Calculate base: (1 + r/n)
var base = 1 + (r_decimal / n);
// Exponentiate: base^n
var powered = Math.pow(base, n);
// Subtract 1
var aer_decimal = powered – 1;
// Convert back to percentage
var aer_percent = aer_decimal * 100;
// 5. Display Results
document.getElementById('aerResult').innerHTML = aer_percent.toFixed(2) + "%";
// Create detailed text comparing Nominal vs AER
var difference = aer_percent – r_percent;
var freqText = document.getElementById('compoundingFreq').options[document.getElementById('compoundingFreq').selectedIndex].text;
var detailHtml = "With a nominal rate of " + r_percent.toFixed(2) + "% compounded " + freqText.split(' ')[0] + ", ";
detailHtml += "the effective yield is " + difference.toFixed(2) + "% higher due to compounding.";
document.getElementById('detailText').innerHTML = detailHtml;
resultSection.style.display = "block";
}