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Equity-Index Annuity (EIA) is a popular annuity in the American and European market.It earns a minimum rate of interest and offers a potential gain that is tied to the performance of a stock index,typically the standard and Poors 500 index.Traditional assumption for the stock index movement is unreasonable for the brusque variations of the stock index because of the important political or nature event.Due to the character of its design,it has a high premium.So lowdown its premium is an important way to bring it more competitive.Giving it an interest cap is a good method to low down its premium.In this paper,we discuss how to price lEA with a cap rate under the indexing methods of point supposed stock index follow jump diffusion process.