Effective Annual Interest Rate

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Effective Annual Interest Rate:

The Effective Annual Interest Rate (EAR) is the interest rate that is adjusted for compounding over a given period. Simply put, the effective annual interest rate is the rate of interest that an investor can earn (or pay) in a year after taking into consideration compounding.

It is also called the effective interest rate, the effective rate, or the annual equivalent rate.

The effective annual interest rate is the real return on a savings account or any interest-paying investment when the effects of compounding over time are taken into account. It also reveals the real percentage rate owed in interest on a loan, a credit card, or any other debt.

The Formula for Effective Annual Interest Rate Is

Effective Annual Interest Rate= (1+ni​)n−1

Where:
i = Stated annual interest rate
n = Number of compounding periods

Example of Effective Annual Interest Rate

For example, consider these two offers: Investment A pays 10% interest, compounded monthly. Investment B pays 10.1% compounded semi-annually. Which is the better offer?
In both cases, the advertised interest rate is the nominal interest rate. The effective annual interest rate is calculated by adjusting the nominal interest rate for the number of compounding periods the financial product will experience in a period of time. In this case, that period is one year. The formula and calculations are as follows:

  • Effective annual interest rate = (1 + (nominal rate / number of compounding periods)) ^ (number of compounding periods) - 1
  • For investment A, this would be: 10.47% = (1 + (10% / 12)) ^ 12 - 1
  • And for investment B, it would be: 10.36% = (1 + (10.1% / 2)) ^ 2 - 1
Investment B has a higher stated nominal interest rate, but the effective annual interest rate is lower than the effective rate for investment A. This is because Investment B compounds fewer times over the course of the year.
If an investor were to put, say, $5,000,000 into one of these investments, the wrong decision would cost more than $5,800 per year.

Another EAR Example:

For example, assume the bank offers your deposit of $10,000 a 12% stated interest rate compounded monthly. The table below demonstrates the concept of the effective annual interest rate:

Month 1 Interest: Beginning Balance ($10,000) x Interest Rate (12%/12 = 1%) = $100

Month 2 Interest: Beginning Balance ($10,100) x Interest Rate (12%/12 = 1%) = $101

The change, in percentage, from the beginning balance ($10,000) to the ending balance ($11,268) is ($11,268 – $10,000)/$10,000 = .12683 or 12.683%, which is the effective annual interest rate. Even though the bank offered a 12% stated interest rate, your money grew by 12.683% due to monthly compounding.

The effective annual interest rate allows you to determine the true return on investment (ROI).

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