This is your actual annual interest rate after compounding.
How to Calculate Effective Rate on a Financial Calculator
Understanding the difference between the nominal rate and the effective rate is crucial for accurate financial modeling. While the nominal rate is the "stated" rate, the effective annual rate (EAR) accounts for the power of compounding during the year.
Using a Texas Instruments BA II Plus
To calculate EAR on a BA II Plus, follow these steps:
Press [2nd] [ICONV] (above the number 2).
NOM: Enter the nominal rate (e.g., 10) and press [ENTER].
Arrow up to C/Y: Enter the number of compounding periods (e.g., 12 for monthly) and press [ENTER].
Arrow to EFF: Press [CPT] to compute the effective rate.
Using an HP 12C
The HP 12C requires a slightly different approach using the interest formula:
Enter the nominal rate as a decimal and divide by periods: [Nominal] [ENTER] [Periods] [รท].
Add 1: [1] [+].
Raise to the power of periods: [Periods] [yx].
Subtract 1: [1] [-].
The Mathematical Formula
If you aren't using a financial calculator, you can use the standard EAR formula:
EAR = (1 + (i / n))n – 1
Where i is the nominal rate and n is the number of compounding periods per year.
Example Calculation
If you have a nominal rate of 12% compounded monthly:
Nominal Rate (i) = 0.12
Periods (n) = 12
EAR = (1 + 0.12/12)12 – 1
EAR = (1.01)12 – 1 = 12.68%
function calculateEffectiveRate() {
var nominalInput = document.getElementById("nominalRate").value;
var compoundingInput = document.getElementById("compoundingPeriods").value;
var resultDisplay = document.getElementById("earResultDisplay");
var resultArea = document.getElementById("ear-result-area");
if (nominalInput === "" || isNaN(nominalInput)) {
alert("Please enter a valid nominal interest rate.");
return;
}
var i = parseFloat(nominalInput) / 100;
var ear = 0;
if (compoundingInput === "continuous") {
// EAR = e^i – 1
ear = Math.exp(i) – 1;
} else {
// EAR = (1 + i/n)^n – 1
var n = parseFloat(compoundingInput);
ear = Math.pow((1 + (i / n)), n) – 1;
}
var finalPercentage = (ear * 100).toFixed(4);
resultDisplay.innerHTML = finalPercentage + "%";
resultArea.style.display = "block";
}