The Annual Percentage Yield (APY) is a standardized way to express the rate of return on an investment or savings account. It takes into account the effect of compounding interest over a full year. Unlike the nominal interest rate, which is the stated rate, APY reflects the actual interest you will earn because it includes the reinvestment of interest earned during the year.
Why APY Matters for Savings Accounts
When comparing different savings accounts, the APY is the most crucial metric. A higher APY means your money grows faster. Even small differences in APY can lead to significant differences in earnings over time, especially with larger balances or longer investment periods.
How APY is Calculated
The APY is calculated using the following formula, which accounts for the principal amount, the nominal interest rate, and how often the interest is compounded within a year:
nominal_interest_rate is the stated annual interest rate (expressed as a decimal).
compounding_frequency is the number of times interest is compounded per year.
While this formula calculates the APY rate itself, our calculator also shows the actual dollar amount earned, which is derived from the APY applied to the initial deposit.
Example Calculation
Let's say you have an initial deposit of $1,000.00, a nominal annual interest rate of 5.00%, and the interest is compounded monthly (12 times per year).
Initial Deposit (Principal): $1,000.00
Nominal Annual Interest Rate: 5.00% (or 0.05 as a decimal)
Compounding Frequency: 12 times per year
First, we calculate the APY rate:
APY = (1 + (0.05 / 12)) ^ 12 - 1
APY = (1 + 0.00416667) ^ 12 - 1
APY = (1.00416667) ^ 12 - 1
APY = 1.05116189 - 1
APY ≈ 0.05116 or 5.116%
Now, to find the actual interest earned in one year using this APY:
Total Amount = Principal * (1 + APY)
Total Amount = $1000.00 * (1 + 0.05116)
Total Amount = $1000.00 * 1.05116
Total Amount = $1051.16
Interest Earned = Total Amount - Principal
Interest Earned = $1051.16 - $1000.00
Interest Earned = $51.16
This calculator will perform these steps to show you the effective APY and the resulting interest earned.
function calculateAPY() {
var principalAmount = parseFloat(document.getElementById("principalAmount").value);
var nominalRate = parseFloat(document.getElementById("nominalRate").value);
var compoundingFrequency = parseInt(document.getElementById("compoundingFrequency").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "; // Clear previous result
if (isNaN(principalAmount) || isNaN(nominalRate) || isNaN(compoundingFrequency) ||
principalAmount <= 0 || nominalRate < 0 || compoundingFrequency <= 0) {
resultDiv.innerHTML = 'Please enter valid positive numbers for all fields.';
return;
}
var nominalRateDecimal = nominalRate / 100;
// Calculate APY Rate
var apyRate = Math.pow((1 + (nominalRateDecimal / compoundingFrequency)), compoundingFrequency) – 1;
// Calculate total amount earned
var totalAmount = principalAmount * (1 + apyRate);
var interestEarned = totalAmount – principalAmount;
// Display results
resultDiv.innerHTML = 'APY Rate: ' + (apyRate * 100).toFixed(4) + '% ' +
'Total Interest Earned in One Year: $' + interestEarned.toFixed(2);
}
function resetForm() {
document.getElementById("principalAmount").value = "";
document.getElementById("nominalRate").value = "";
document.getElementById("compoundingFrequency").value = "";
document.getElementById("result").innerHTML = "";
}