How to Calculate Effective Annual Rate in Excel – Cost Calculator

Effective Annual Rate (EAR) Calculator

Nominal Annual Interest Rate (%):

Number of Compounding Periods per Year:

Result:

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 actual rate of return earned on an investment or paid on a loan over a one-year period, taking into account the effects of compounding. While a nominal interest rate might be quoted, it doesn't always reflect the true cost or yield because interest can be compounded more frequently than once a year.

Why EAR Matters

Compounding is the process where interest earned is added to the principal, and subsequent interest is calculated on this new, larger principal. The more frequently interest is compounded (e.g., monthly, quarterly, daily), the greater the impact of compounding. The EAR normalizes these different compounding frequencies into a single, comparable annual rate.

For Investors: EAR shows the true growth of your investment over a year. A higher EAR means your money is working harder for you.
For Borrowers: EAR reveals the true cost of borrowing. A loan with a lower EAR is more advantageous, even if its nominal rate appears similar to another loan.

How to Calculate EAR

The formula for calculating the EAR is:

EAR = (1 + (Nominal Rate / n))^n – 1

Where:

Nominal Rate is the stated annual interest rate.
n is the number of compounding periods per year.

For example, if interest is compounded monthly, n would be 12. If compounded quarterly, n would be 4. If compounded annually, n would be 1.

Using the Calculator

Our EAR calculator simplifies this process. Simply input the nominal annual interest rate and the number of times that interest is compounded within a year. The calculator will then provide you with the effective annual rate, allowing for a clear comparison of different financial products.

Example Calculation:

Let's say you have an investment with a nominal annual interest rate of 5.00% that compounds monthly.

Nominal Annual Interest Rate: 5.00%
Number of Compounding Periods per Year: 12

Using the formula:

EAR = (1 + (0.05 / 12))^12 – 1

EAR = (1 + 0.00416667)^12 – 1

EAR = (1.00416667)^12 – 1

EAR = 1.0511619 – 1

EAR = 0.0511619

So, the Effective Annual Rate is approximately 5.12%.

This means that while the nominal rate is 5%, the actual yield over a year due to monthly compounding is slightly higher, at 5.12%.

function calculateEAR() { var nominalRateInput = document.getElementById("nominalRate"); var compoundingPeriodsInput = document.getElementById("compoundingPeriods"); var earResultDisplay = document.getElementById("earResult"); var nominalRate = parseFloat(nominalRateInput.value); var compoundingPeriods = parseInt(compoundingPeriodsInput.value); if (isNaN(nominalRate) || isNaN(compoundingPeriods) || compoundingPeriods <= 0) { earResultDisplay.textContent = "Please enter valid numbers for both fields, and ensure the number of compounding periods is greater than zero."; return; } var ratePerPeriod = nominalRate / 100 / compoundingPeriods; var effectiveRate = Math.pow(1 + ratePerPeriod, compoundingPeriods) – 1; earResultDisplay.textContent = (effectiveRate * 100).toFixed(2) + "%"; }