In this paper, we study upper and lower bounds on the achievable sum-rate of an uncorrelated multiple-input multiple-output (MIMO) multiple access channel (MAC) for Gaussian input signals and with channel estimation error at the receiver. We prove that the gap between the mutual information hounds does not exceed a certain value for arbitrary input covariance matrices and at any input transmit power. We also prove that in a MIMO MAC with uniform input power utilization over the transmit antennas, the gap between the mutual information bounds increases monotonically as the input power of each user increases. Furthermore, we show that the gap between the bounds is maximum when beamforming is applied at the transmitters of all users. We also derive the transmit directions that maximize the mutual information lower and upper bounds when delayed feedback is available from the receiver to the transmitters, and characterize the power allocation of this system in terms of its beamforming range. Numerical simulations are conducted to corroborate our theoretical results and quantify the effect of imperfect channel estimation.