Many philosophers are sympathetic to a perdurantist view of persistence. One challenge facing this view lies in its ability to ground prudential rationality. If, as many have thought, numerical identity over time is required to ground there being sui generis (i.e. non-instrumental) prudential reasons, then perdurantists can appeal only to instrumental reasons. The problem is that it is hard to see how, by appealing only to instrumental reasons, the perdurantist can vindicate the axiom of prudence: the axiom that any person-stage has reason to promote the wellbeing of any other person-stage that is part of the same person as that stage. The claim that perdurantists cannot vindicate the axiom, and hence that the view should be rejected, is what we call the normative argument against perdurantism. In this paper we argue that purely instrumental rationality can ground the truth of this axiom, and hence that the normative argument against perdurantism fails.