The no arbitrage pricing of Guaranteed Minimum Withdrawal Benefits (GMWB) contracts results in a singular stochastic control problem which can be formulated as a Hamilton Jacobi Bellman (HJB) Variational Inequality (VI). Recently, a penalty method has been suggested for solution of this HJB variational inequality (Dai et al, 2008). This method is very simple to implement. In this talk, we present a rigorous proof of convergence of the penalty method to the viscosity solution of the HJB VI. Numerical tests of the penalty method are presented which show the experimental rates of convergence, and a discussion of the choice of the penalty parameter is also included. A comparsion with an impluse control formulation of the same problem, in terms of generality and computational complexity, is also presented.