We present proper motion measurements of the oxygen-rich ejecta of the LMC supernova remnant N132D using two epochs of Hubble Space Telescope Advanced Camera for Surveys data spanning 16 years. The proper motions of 120 individual knots of oxygen-rich gas were measured and used to calculate a center of expansion (CoE) of {alpha}=5h25m01.71s and {delta}=-69{deg}38'41.64" (J2000) with a 1{sigma} uncertainty of 2.90". This new CoE measurement is 9.2" and 10.8" from two previous CoE estimates based on the geometry of the optically emitting ejecta. We also derive an explosion age of 2770+/-500yr, which is consistent with recent age estimates of ~2500yr made from 3D ejecta reconstructions. We verified our estimates of the CoE and age using a new automated procedure that detected and tracked the proper motions of 137 knots, with 73 knots that overlap with the visually identified knots. We find that the proper motions of the ejecta are still ballistic, despite the remnant's age, and are consistent with the notion that the ejecta are expanding into an interstellar medium cavity. Evidence for explosion asymmetry from the parent supernova is also observed. Using the visually measured proper motion measurements and corresponding CoE and age, we compare N132D to other supernova remnants with proper motion ejecta studies.