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This paper introduces some novel upper and lower bounds on the achievable sum rate of multiple-input multiple-output (MIMO) systems with zero-forcing (ZF) receivers. The presented bounds are not only tractable but also generic since they apply for different fading models of interest, such as uncorrelated/correlated Rayleigh fading and Ricean fading. We further formulate a new relationship between the sum rate and the first negative moment of the unordered eigenvalue of the instantaneous correlation matrix. The derived expressions are explicitly compared with some existing results on MIMO systems operating with optimal and minimum mean-squared error (MMSE) receivers. Based on our analytical results, we gain valuable insights into the implications of the model parameters, such as the number of antennas, spatial correlation and Ricean-K factor, on the sum rate of MIMO ZF receivers.