# The Effective Annual Rate (EAR)

Think effective annual rate synonymously with compounding of interest rates. This effective annual rate (EAR) can be defined mathematically. Although, we can save the formula from the article for the interest of explanation of the meaning of compounding growth.

Essentially, the compounding of interest is the accelerated earning of a sum of money. Ensuing years from time of initial investment increases the rate of interest earned because the principal sum is becoming larger. This increasing sum of money being added to the account makes in the interest payment larger each year.

The method of exponential compounding has been described in a parable. In an old kingdom in history a man had wagered to a wealthy prince his ability to solve a math problem and won. The wealthy prince had promised to pay a grain of rice doubling the amount for each square on a chess board. In other words, at a 100% interest rate he promised to compound sixty-four payments of rice. He though that starting from a grain of rice there would be only a small payment. However, the wealthy prince had not even enough rice to pay the sum.

Mathematically that exponential compounding would equate to the following:

2^64 = 18,446,740,000,000,000,000 grains! 