Effective Annual Rate Calculator

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Effective Annual Rate (EAR) Calculator

Understanding the Effective Annual Rate (EAR)

The Effective Annual Rate (EAR), also known as the Annual Equivalent Rate (AER) or effective interest rate, is a crucial concept in finance that represents the real rate of return earned on an investment or paid on a loan, taking into account the effects of compounding interest over a year.

While the nominal interest rate is the stated interest rate before accounting for compounding, the EAR provides a more accurate picture of the actual interest you will earn or pay. This is because most financial products compound interest more frequently than once a year (e.g., monthly, quarterly, or semi-annually). Each compounding period recalculates interest based on the current balance, which includes previously earned interest. This phenomenon is known as compounding.

Why is EAR Important?

  • Accurate Comparison: EAR allows for a standardized comparison of different investment or loan products with varying compounding frequencies. A product with a slightly lower nominal rate but more frequent compounding might yield a higher effective return than a product with a higher nominal rate compounded less often.
  • Investment Returns: For investors, understanding the EAR helps in projecting the true growth of their investments over time.
  • Loan Costs: For borrowers, the EAR reveals the actual cost of a loan, which can significantly differ from the advertised nominal rate, especially for high-frequency compounding.

How to Calculate EAR

The formula to calculate the Effective Annual Rate is:

EAR = (1 + (i/n))^n – 1

Where:

  • i is the nominal annual interest rate (expressed as a decimal).
  • n is the number of compounding periods per year.

For example, if a bank offers a savings account with a nominal annual interest rate of 5% compounded monthly:

  • The nominal rate (i) as a decimal is 0.05.
  • The number of compounding periods per year (n) is 12 (for monthly compounding).

Using the formula:

EAR = (1 + (0.05/12))^12 – 1

EAR = (1 + 0.00416667)^12 – 1

EAR = (1.00416667)^12 – 1

EAR = 1.051161897 – 1

EAR = 0.051161897

Converting this decimal back to a percentage, the EAR is approximately 5.12%. This means that despite the nominal rate being 5%, the actual return after monthly compounding is 5.12% per year.

Our calculator above simplifies this process, allowing you to quickly determine the EAR for any given nominal rate and compounding frequency.

function calculateEAR() { var nominalRateInput = document.getElementById("nominalRate"); var compoundingPeriodsInput = document.getElementById("compoundingPeriods"); var resultDiv = document.getElementById("result"); var nominalRate = parseFloat(nominalRateInput.value); var compoundingPeriods = parseFloat(compoundingPeriodsInput.value); if (isNaN(nominalRate) || isNaN(compoundingPeriods) || compoundingPeriods <= 0) { resultDiv.innerHTML = "Please enter valid numbers for the nominal rate and a positive number for compounding periods."; return; } var rateDecimal = nominalRate / 100; var ear = Math.pow((1 + rateDecimal / compoundingPeriods), compoundingPeriods) – 1; resultDiv.innerHTML = "The Effective Annual Rate (EAR) is: " + (ear * 100).toFixed(4) + "%"; }

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