Technically, this is a form of a fixed, rather than a variable annuity, but your return is tied to a stock index (e.g., the S&P 500) that provides the opportunity to earn a return that is better than the traditional fixed annuity. The purchaser does not choose investments, but is able to participate in the stock market to some degree, with a guaranteed minimum return (typically around 3%).
One confusing feature of an equity-indexed annuity (EIA) is the method used to calculate the gain in the index to which the annuity is linked. There are several different indexing methods that companies use. Because of the variety and complexity of the methods used to credit interest, it may be difficult to compare one EIA to another.
It is possible to lose money in an EIA, since some companies guarantee a minimum return of only 90% of the premium plus the guaranteed annual interest rate. As with all annuities, early withdrawal can also result in a loss.
EIAs carry more risk (but more potential return when the stock market rises) than a fixed annuity, but because of the guaranteed interest rate, they have less risk (as well as less potential return) than a variable annuity.