Interest is payment for the use of money, such as when someone takes out a loan or if a person places an amount in an interest-bearing account. The effective annual yield is the rate of interest received when the method of compounding the interest is included. Compound interest is computed on both principal and accumulated interest.
The first step to arrive at the effective annual interest rate is to take the stated annual interest rate and divide it by the number of compounding periods. One is then added and the result is taken to the power of the number of compounding periods. One is then subtracted from this result. In formula format this would look like: (1 + i/n)^n -1, where "i" is the stated interest rate and "n" is the number of compounding periods.
Stated interest rate is the interest rate that is normally displayed and does not take into consideration how many times the interest is compounded. If a person begins with $100 US Dollars (USD) and the stated rate is 5 percent, the amount at the end of the year without compounding the interest would be $105 USD. Results are larger if compound interest is used. For example, $100 USD at 5 percent interest compounded monthly would result in $105.12 USD and the effective rate would be 5.11619 percent.
The more often the interest is compounded, the larger the result and the higher the effective annual yield would be. For example, using the above principle and interest and compounding daily instead of monthly, the result would be 5.126750 percent and the dollar amount would increase to $105.13 USD. If the principle is much greater, the difference in the effective annual yield will be too.
Annual effective rate (AER) refers to the interest rate on a loan that has been restated from the amount listed without reference to inflation or compounding to an interest rate that includes the compounding. Moreover, the effective annual yield is the amount that a person receives in income over a period of a year. The reason the effective rate is greater than the stated or nominal rate is that with each compounding period the interest is added to the principle and future interest will be on both principle and previous interest.
Whether taking out a loan or investing money, it can be important for a person to compare the effective annual yield or rate. This is due to the fact that the amount of interest will be different depending on whether the interest is compounded daily, weekly, monthly, or annually. The more often interest is compounded, the higher the effective annual yield will be.