Combinations of non-trivial band topology and long-range magnetic order hold promise for realizations of novel spintronic phenomena, such as the quantum anomalous Hall effect and the topological magnetoelectric effect. Following theoretical advances material candidates are emerging. Yet, a compound with a band-inverted electronic structure and an intrinsic net magnetization remains unrealized. MnBi$_2$Te$_4$ is a candidate for the first antiferromagnetic topological insulator and the progenitor of a modular (Bi$_2$Te$_3$)$_n$(MnBi$_2$Te$_4$) series. For $n$ = 1, we confirm a non-stoichiometric composition proximate to MnBi$_4$Te$_7$ and establish an antiferromagnetic state below 13 K followed by a state with net magnetization and ferromagnetic-like hysteresis below 5 K. Angle-resolved photoemission experiments and density-functional calculations reveal a topological surface state on the MnBi$_4$Te$_7$(0001) surface, analogous to the non-magnetic parent compound Bi$_2$Te$_3$. Our results render MnBi$_4$Te$_7$ as a band-inverted material with an intrinsic net magnetization and a complex magnetic phase diagram providing a versatile platform for the realization of different topological phases.
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