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We consider model predictive control (MPC) problems with linear dynamics, polytopic constraints and quadratic objective. The resulting optimization problem is solved by applying an accelerated gradient method to the dual problem. The focus of this paper is to provide bounds on the number of iterations needed in the algorithm to guarantee a prespecified accuracy of the dual function value and the primal variables as well as guaranteeing a prespecified maximal constraint violation. The provided numerical example shows that the iteration bounds are tight enough to be useful in an inverted pendulum application.