When you're looking at savings accounts, bonds, or other financial products, you'll often see two different rates: the Nominal Annual Interest Rate and the Annual Percentage Yield (APY). While they sound similar, they represent different ways of measuring the return on your investment.
Nominal Annual Interest Rate
The nominal annual interest rate is the simple, stated interest rate before taking into account the effect of compounding. It tells you the rate of interest you'd earn in a year if interest were only calculated and paid once at the end of the year. For example, a 5% nominal rate means you'd earn 5% of your principal in interest over a year, assuming no compounding within that year.
The formula for the periodic interest rate is:
Periodic Rate = Nominal Annual Interest Rate / Number of Compounding Periods per Year
Annual Percentage Yield (APY)
The APY, on the other hand, reflects the true rate of return considering the effect of compounding interest. Compounding means that you earn interest not only on your initial principal but also on the accumulated interest from previous periods. The more frequently interest is compounded, the higher the APY will be compared to the nominal rate.
This calculator helps you see the effective growth of your investment by converting a nominal rate, based on its compounding frequency, into its equivalent APY.
The APY Formula
The formula used to calculate APY is:
APY = (1 + (Nominal Rate / n))^n - 1
Where:
Nominal Rate is the stated annual interest rate (expressed as a decimal, e.g., 5% = 0.05).
n is the number of times the interest is compounded per year.
For example, if you have a nominal rate of 5% compounded monthly:
Nominal Rate = 0.05
n = 12 (monthly compounding)
APY = (1 + (0.05 / 12))^12 – 1
APY = (1 + 0.00416667)^12 – 1
APY = (1.00416667)^12 – 1
APY = 1.05116189 – 1
APY = 0.05116189, or approximately 5.12%
As you can see, the APY (5.12%) is higher than the nominal rate (5%) due to the effect of monthly compounding.
Why APY Matters
When comparing different financial products, always look at the APY. It provides a standardized way to compare the actual returns you can expect, regardless of how often the interest is compounded. A higher APY generally means your money grows faster.
function calculateAPY() {
var nominalRateInput = document.getElementById("nominalRate");
var compoundingFrequencyInput = document.getElementById("compoundingFrequency");
var resultDiv = document.getElementById("result");
var resultValueDiv = document.getElementById("result-value");
var nominalRate = parseFloat(nominalRateInput.value);
var n = parseInt(compoundingFrequencyInput.value);
if (isNaN(nominalRate) || isNaN(n) || nominalRate < 0 || n <= 0) {
alert("Please enter valid numbers for nominal rate and compounding frequency.");
resultDiv.style.display = 'none';
return;
}
// Convert nominal rate percentage to decimal
var rateDecimal = nominalRate / 100;
// Calculate APY using the formula: APY = (1 + (nominalRate / n))^n – 1
var apy = Math.pow((1 + (rateDecimal / n)), n) – 1;
// Format APY to percentage with 2 decimal places
var formattedApy = (apy * 100).toFixed(2);
resultValueDiv.textContent = formattedApy + "%";
resultDiv.style.display = 'block';
}