We studied the possibility of achieving an order of magnitude reduction in the energy dissipation needed to write bits in perpendicular magnetic tunnel junctions (p-MTJs) by simulating the magnetization dynamics under a combination of resonant surface acoustic waves (r-SAW) and spin-transfer-torque (STT). The magnetization dynamics were simulated using the Landau-Lifshitz-Gilbert equation under macrospin assumption with the inclusion of thermal noise. We studied such r-SAW assisted STT switching of nanomagnets for both in-plane elliptical and circular perpendicular magnetic anisotropy (PMA) nanomagnets and show that while thermal noise affects switching probability in in-plane nanomagnets, the PMA nanomagnets are relatively robust to the effect of thermal noise. In PMA nanomagnets, the resonant magnetization dynamics builds over few 10s of cycles of SAW application that drives the magnetization to precess in a cone with a deflection of ~45⁰ from the perpendicular direction. This reduces the STT current density required to switch the magnetization direction without increasing the STT application time or degrading the switching probability in the presence of room temperature thermal noise. This could lead to a pathway to achieve energy efficient switching of spin-transfer-torque random access memory (STT-RAM) based on p-MTJs whose lateral dimensions can be scaled aggressively despite using materials with low magnetostriction by employing resonant excitation to drive the magnetization away from the easy axis before applying spin torque to achieve a complete reversal.