The MACE (Major Atmospheric Cherenkov Experiment) is an upcoming Very High Energy (VHE) gamma-ray telescope, based on imaging atmospheric Cherenkov technique, being installed at Hanle, a high altitude astronomical site in Ladakh, India. Here we present Monte Carlo simulation studies of trigger rates and threshold energies of MACE in the zenith angle range of 0 degrees-60 degrees for on-axis gamma-ray coming from point source and various cosmic ray species. We have simulated the telescope's response to gamma-rays, proton, electron and alpha initiated atmospheric Extensive Air Showers (EAS) in the broad energy range of 5 GeV to 20 TeV. For gamma-rays we consider power law and log parabolic spectra while other particles are simulated with their respective cosmic ray spectrum. Trigger rates and threshold energies are estimated for the trigger configuration of 4 Close Cluster Nearest Neighbour(CCNN) pixels as implemented in MACE hardware, in combination with single channel discriminator threshold ranging from 6-10 photo electrons (pe). We find that MACE can achieve the gamma-ray trigger energy threshold of similar to 17 GeV (4 CCNN, 9 pe) at 0 degrees zenith angle for power law spectrum. The total trigger rate at 0 degrees zenith is expected to be similar to 650 Hz, with protons contributing similar to 80% to it. For the zenith range of 0 degrees-40 degrees we find that the telescope can achieve gamma-gray trigger threshold energies of similar to 22 GeV at 20 degrees zenith angle and similar to 40 GeV at 40 degrees zenith angle. Integral rates are also almost constant for this zenith angle range. At zenith angle of 60 degrees, trigger energy threshold increases to similar to 173 GeV and total integral rate falls down to similar to 305 Hz. (C) 2016 Elsevier B.V. All rights reserved.