All rings in this paper are commutative, with identity. If the ring R is either finitely generated, or semi-local (by which I mean Noetherian and possessing only finitely many maximal ideals), then R has only a finite number of ideals of each finite index. Thus it makes sense to study the function n[map ]an(R), where an(R) denotes the number of ideals of index n in R. In an earlier note [10], I determined an(R) for certain 2-dimensional domains R. The results to be discussed here are less precise, but more general; in particular, they deal with submodules of a finitely generated module. This makes it possible to translate them into results about the growth of normal subgroups in certain metabelian groups, the original motivation for this work: for example, we determine the finitely generated metabelian groups with ‘polynomial normal subgroup growth’ (Theorem 6.1).