We study the influence of a second order magnetic anisotropy on magnetization reversal by spin transfer torque in perpendicularly magnetized magnetic tunnel junctions (pMTJs). Using a macrospin model to describe the dynamics of the free layer, analytical solutions for the switching voltage and the voltage threshold for precession are determined as a function of the first and second order magnetic anisotropies. To compare the spin-transfer-torque energy efficiency to that of a classical pMTJ, a junction without the second order anisotropy term, we compare these cases at a fixed energy barrier to thermally activated reversal. We show that the critical voltage for switching can be reduced by a factor 0.7 when the ratio of the second to the first order magnetic anisotropy is 1/3. Importantly, the switching time can be reduced by nearly a factor of two for this magnetic anisotropy ratio. These results highlight an important and practical method to increase the spin-torque efficiency, while reducing the energy dissipation and switching time in magnetic random access memory devices.