Annual Percentage Yield Calculator

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Annual Percentage Yield (APY) Calculator
Calculate APY (from APR)Calculate APR (from APY)
Daily (365/yr)Monthly (12/yr)Quarterly (4/yr)Semi-Annually (2/yr)Annually (1/yr)Daily (360/yr)
Result:
function toggleInputs(){var type=document.getElementById('calc_type').value;var l1=document.getElementById('label1′);if(type==='apy_from_apr'){l1.innerHTML='Nominal Rate (APR): %';}else{l1.innerHTML='Effective Rate (APY): %';}}function calculateResult(){var type=document.getElementById('calc_type').value;var rate=parseFloat(document.getElementById('input1').value);var n=parseFloat(document.getElementById('input2').value);var showSteps=document.getElementById('steps').checked;if(isNaN(rate)||isNaN(n)){alert('Please enter valid numeric values');return;}var r=rate/100;var result=0;var details="";if(type==='apy_from_apr'){result=(Math.pow(1+(r/n),n)-1)*100;if(showSteps){details="Step 1: Convert APR to decimal: "+rate+"% / 100 = "+r+"
";details+="Step 2: Divide rate by compounding periods: "+r+" / "+n+" = "+(r/n).toFixed(6)+"
";details+="Step 3: Add 1: 1 + "+(r/n).toFixed(6)+" = "+(1+(r/n)).toFixed(6)+"
";details+="Step 4: Raise to power of n ("+n+"): "+Math.pow(1+(r/n),n).toFixed(8)+"
";details+="Step 5: Subtract 1 and convert to percentage: ("+Math.pow(1+(r/n),n).toFixed(8)+" – 1) * 100 = "+result.toFixed(4)+"%";}document.getElementById('summary').innerHTML="APY = "+result.toFixed(4)+"%";}else{result=n*(Math.pow((r+1),(1/n))-1)*100;if(showSteps){details="Step 1: Convert APY to decimal: "+rate+"% / 100 = "+r+"
";details+="Step 2: Add 1: 1 + "+r+" = "+(r+1)+"
";details+="Step 3: Take the "+n+"-th root: "+Math.pow((r+1),(1/n)).toFixed(8)+"
";details+="Step 4: Subtract 1: "+(Math.pow((r+1),(1/n))-1).toFixed(8)+"
";details+="Step 5: Multiply by n ("+n+") and convert to %: "+result.toFixed(4)+"%";}document.getElementById('summary').innerHTML="APR = "+result.toFixed(4)+"%";}if(showSteps){document.getElementById('stepDetails').innerHTML=details;document.getElementById('stepDetails').style.display='block';}else{document.getElementById('stepDetails').style.display='none';}}

Calculator Use

The annual percentage yield calculator is a financial tool designed to help you determine the real rate of return on an investment or the true cost of a loan. While banks often advertise the nominal interest rate (APR), the APY reflects the effect of compounding interest throughout the year. Use this tool to compare different financial products that have varying compounding frequencies, such as daily, monthly, or quarterly.

Nominal Rate (APR)
The stated annual interest rate that does not take into account the compounding of interest within that year.
Compounding Periods
The frequency at which interest is calculated and added back to the principal balance (e.g., 12 times per year for monthly compounding).
Effective Rate (APY)
The actual annual rate of return, including the effect of compounding interest.

How It Works

To understand the math behind our annual percentage yield calculator, you need to look at how interest builds upon interest. The more frequently interest is compounded, the higher the APY will be relative to the APR. The standard formula used by this calculator is:

APY = (1 + r/n)n – 1

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

Calculation Example

Example: Imagine you open a high-yield savings account that offers a 5.00% nominal APR compounded monthly. You want to find out what your actual yield will be at the end of one year.

Step-by-step solution:

  1. Nominal Rate (r) = 5.00% = 0.05
  2. Compounding Periods (n) = 12 (monthly)
  3. Divide rate by periods: 0.05 / 12 = 0.0041667
  4. Add 1 to the result: 1 + 0.0041667 = 1.0041667
  5. Raise to the 12th power: (1.0041667)12 = 1.0511619
  6. Subtract 1: 1.0511619 – 1 = 0.0511619
  7. Result: The APY is 5.116%

Common Questions

What is the difference between APR and APY?

APR (Annual Percentage Rate) is the simple interest rate over a year. APY (Annual Percentage Yield) is the interest rate taking into account the effect of compound interest. APY will always be equal to or higher than the APR. Financial institutions often show the APR for loans (to make the rate look lower) and the APY for savings accounts (to make the return look higher).

How does compounding frequency affect my yield?

The more often interest compounds, the higher your APY. For example, a 10% APR compounded annually results in a 10% APY. However, if that same 10% is compounded daily, the APY rises to approximately 10.517%. This occurs because you are earning interest on the interest earned in previous days.

Why is APY important for investors?

APY provides a standardized way to compare the yields of different investments. Without using an annual percentage yield calculator, it is difficult to determine whether a 4.5% rate compounded daily is better than a 4.6% rate compounded annually. APY levels the playing field so you can see which investment actually grows your money faster.

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