The concept of a time-relative interest is introduced by Jeff McMahan to solve certain puzzles about the badness of death. Some people (e.g. McMahan and David DeGrazia) believe that this concept can also be used to show that abortion is permissible. In this paper, I first argue that if the Time-Relative Interest Account permits abortion, then it would also permit infanticide. I next reject the suggestion that the Time-Relative Interest Account can at least explain the permissibility of early abortion, even if it cannot explain the permissibility of late abortion. Given this, early and late abortions have to be justified on other grounds.