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Given a matrix   $A\in SL(N,\mathbb{Z})$  , form the semidirect product   $G=\mathbb{Z}^N\rtimes_A \mathbb{Z}$   where the   $\mathbb{Z}$  -factor acts on   $\mathbb{Z}^N$   by   $A$  . Such a   $G$   arises naturally as the fundamental group of an   $N$  -dimensional torus bundle which fibers over the circle. In this article, we prove that if   $A$   has distinct eigenvalues not lying on the unit circle, then there exists a finite index subgroup   $H\leq G$   possessing rational growth series for some generating set. In contrast, we show that if   $A$   has at least one eigenvalue not lying on the unit circle, then   $G$   is not almost convex for any generating set.

Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles