Accumulator is a highly path dependant derivative structure, whose underlying assets can be currency rate, stock price, power source and so on. This paper studies the accumulator pricingproblems under different setting of the contract. First, we review pricing an accumulator in which the barrier is applied continuously. Second, without analytical formulae, the price of an accumulator with barrier applied discretely has to be determined by approximation or numerical methods. The Fourier cosine expansions method, initiated by Fang and Oosterlee [SIAM Journal on Scientific Computing, 31(2), 826-848], is applied to present a numerical method to solve it. The numerical results, compared with Barrier Correction method and Monte Carlo simulation method, are given to show the efficiency of the presented method. The last part gives a financial analysis about the risk hidden in anaccumulator.