An effective annual return accounts for the effects of compounding when determining interest earnings over the course of a year. Sometimes it is easy to determine this rate, because interest may only be compounded once a year. In other cases, it can require a formula to consider the number of compounding periods. It is important to know when interest is compounded when thinking about interest earnings on savings and other investments, as well as interest that will be paid out on debts.
For the purpose of this calculation, analysts assume that all the money will be left in place, with no withdrawals to complicate interest calculations. In a simple example, Sally could open a savings account with $100 United States Dollars (USD). The bank offers her 5% interest and compounds annually. Her effective annual return is 5%, because when they compound her interest at the end of the year, assuming she left all her money in the bank, she will have $105 USD.
If, however, the bank compounds interest twice a year, the rate changes. She will end up with slightly more at the end of the year, because the interest compounded in the first part of the year will in turn earn money during the second part of the year. If the bank compounds quarterly or monthly, she’ll earn even more. The more often the bank compounds, the more money she can earn, because her interest will earn interest.
One formula people can use to determine the effective annual return is: (1+i/n)n-1. The i in the formula stands for the interest rate, while n reflects the number of compounding periods. For Sally’s savings account compounded monthly, for example, the formula would look like this: (1+0.05/12)12-1, or 0.051. She’d be earning just over 5% in interest every year. Her effective annual return would increase with the interest rate or number of compounding periods, earning even more money.
In account disclosures with information about the benefits available, a variety of terms may be used to discuss interest and earnings. These are often presented in a way that makes an account look as enticing as possible. They are not necessarily comparable between account offers, unless the same terminology is being used. Calculating effective annual return can help people better understand their earnings with different kinds of accounts. Using the formula above, it’s possible to quickly compare accounts on the basis of the stated information, as the contract should discuss the interest rate and number of compounding periods.