Abstract: The study of interest randomness is one of the heated and major problems of actuarial science in recent years. In this paper, giving a class of increasing payments life insurance and considing abrupt event’s effect on interest, we establish the model for stochastic interest jointly by both Gauss process and Poisson process, and give all orders moment of payable present value of immediately payable increasing life insurance. Finally, the concise expressions are given in some special cases.