Rate to Yield Calculator

Rate to Yield Calculator

Annually (1/year) Semi-Annually (2/year) Quarterly (4/year) Monthly (12/year) Weekly (52/year) Daily (365/year) Hourly (8760/year) Continuous

Effective Annual Yield (APY)

0.00%

Understanding Rate vs. Yield

While the Nominal Annual Rate (APR) is the "sticker price" of an investment or debt, the Effective Annual Yield (APY) represents the actual economic reality. The difference between the two is caused by compounding frequency.

The Mathematical Formula

Yield = (1 + (r / n))^n – 1

Where:

• r = The nominal annual interest rate (as a decimal)
• n = The number of compounding periods per year

Real-World Example

Imagine you have a savings account with a 5% nominal rate. Depending on how often the bank calculates interest, your actual yield changes:

Compounding	Annual Yield
Annually	5.00%
Monthly	5.116%
Daily	5.127%

Why This Matters for Investors

When comparing financial products, always look at the Yield rather than the Rate. A lower nominal rate with frequent compounding (like daily) can sometimes result in a higher actual return than a higher nominal rate that only compounds annually. This calculator helps you normalize different offers to make an "apples-to-apples" comparison.

function calculateEffectiveYield() { var nominalRateInput = document.getElementById("nominalRate").value; var periods = parseFloat(document.getElementById("compoundingPeriods").value); var resultWrapper = document.getElementById("yieldResultWrapper"); var yieldValueDisplay = document.getElementById("yieldValue"); var yieldComparison = document.getElementById("yieldComparison"); if (nominalRateInput === "" || isNaN(nominalRateInput)) { alert("Please enter a valid nominal rate."); return; } var r = parseFloat(nominalRateInput) / 100; var yieldResult; // Check if user selected Continuous Compounding (marked as 1,000,000 for simplicity) if (periods >= 1000000) { // Formula for continuous compounding: e^r – 1 yieldResult = Math.exp(r) – 1; } else { // Standard discrete compounding formula: (1 + r/n)^n – 1 yieldResult = Math.pow((1 + (r / periods)), periods) – 1; } var finalPercentage = (yieldResult * 100).toFixed(4); var difference = (finalPercentage – (r * 100)).toFixed(4); yieldValueDisplay.innerText = finalPercentage + "%"; yieldComparison.innerText = "This is " + difference + "% higher than your nominal rate due to compounding."; resultWrapper.style.display = "block"; // Scroll result into view if mobile if (window.innerWidth < 600) { resultWrapper.scrollIntoView({ behavior: 'smooth' }); } }