Before revision:  An optimal convergence rate for this sequence is found and sharp computable upper bounds for the approximation accuracy of the optimal consumption - investment strategies are obtained. It turns out that the optimal  convergence rate in this case is super geometrical, i.e. is more rapid than any geometrical rate .
After revision:  An optimal convergence rate of the iterative numerical schemes for both the value function and the optimal convergence rate in this case is super geometrical, i.e. is more rapid than any geometrical rate .