Annually (1x per year)
Semi-Annually (2x per year)
Quarterly (4x per year)
Monthly (12x per year)
Semi-Monthly (24x per year)
Bi-Weekly (26x per year)
Weekly (52x per year)
Daily (365x per year)
Continuously
Effective Annual Yield (APY)
0.00%
function calculateAPY() {
var nominalRateInput = document.getElementById("nominalRate").value;
var freqInput = document.getElementById("compoundingFreq").value;
// Validation
if (nominalRateInput === "" || nominalRateInput < 0) {
alert("Please enter a valid positive nominal interest rate.");
return;
}
var r = parseFloat(nominalRateInput) / 100; // Convert percentage to decimal
var n = parseFloat(freqInput); // Number of compounding periods
var apy;
// Continuous compounding calculation logic vs standard discrete
if (n === 36525) {
// Continuous compounding: APY = e^r – 1
apy = Math.exp(r) – 1;
} else {
// Standard formula: APY = (1 + r/n)^n – 1
apy = Math.pow((1 + (r / n)), n) – 1;
}
// Convert back to percentage
var apyPercent = apy * 100;
// Calculate difference (Basis Points)
var difference = apyPercent – parseFloat(nominalRateInput);
// Display Results
var resultBox = document.getElementById("resultBox");
var apyDisplay = document.getElementById("apyResult");
var diffDisplay = document.getElementById("differenceResult");
resultBox.style.display = "block";
apyDisplay.innerHTML = apyPercent.toFixed(4) + "%";
diffDisplay.innerHTML = "Increase over Nominal Rate: " + difference.toFixed(4) + "%";
}
Understanding Effective Annual Rate (APY)
The Effective Annual Yield, commonly known as APY (Annual Percentage Yield), is a crucial financial metric that reveals the true rate of return on an investment or the true interest rate on a loan after accounting for the effects of compounding interest. While the nominal interest rate (APR) is the "headline" rate, the APY tells you what your money is actually earning (or costing) over the course of a year.
Key Concept: The more frequently interest is compounded, the higher the Effective Annual Rate will be compared to the Nominal Rate.
Nominal Rate (APR) vs. Effective Rate (APY)
It is easy to confuse APR and APY, but the difference can significantly impact your financial planning:
Nominal Rate (APR): This is the simple interest rate stated by the bank or lender. It does not account for compounding periods within the year.
Effective Rate (APY): This is the actual rate earned or paid. It assumes that the interest earned is reinvested (compounded) at the same rate.
The Effective Rate Formula
The standard formula used by this calculator to determine the effective annual rate is:
APY = (1 + r/n)n – 1
Where:
r = The nominal annual interest rate (in decimal form).
n = The number of compounding periods per year.
Impact of Compounding Frequency
To demonstrate how compounding frequency changes the effective rate, let's look at an example using a 5% Nominal Rate:
Compounding Frequency
Nominal Rate
Effective Rate (APY)
Annually (1x)
5.00%
5.0000%
Semi-Annually (2x)
5.00%
5.0625%
Quarterly (4x)
5.00%
5.0945%
Monthly (12x)
5.00%
5.1162%
Daily (365x)
5.00%
5.1267%
Why Is This Calculator Useful?
For Savers: Banks often advertise the APY on savings accounts and CDs because it looks higher than the APR. However, if you are comparing two accounts where one lists APR and the other lists APY, you need to convert them to the same metric to make a fair comparison.
For Borrowers: Lenders (especially for credit cards and mortgages) prefer to advertise the APR because it looks lower. Using an Effective Rate Calculator helps you understand the true cost of borrowing when interest is added to your principal balance monthly or daily.
Frequently Asked Questions
Does a higher compounding frequency always mean a higher return?
Yes, assuming the nominal rate remains the same. Daily compounding will yield more than monthly compounding, which yields more than annual compounding.
What is continuous compounding?
Continuous compounding is the mathematical limit that compound interest can reach if it's calculated and reinvested every possible instant. The formula changes to APY = er – 1.