In this paper, we study the spectral efficiency (SE) of a multi-cell massive multiple-input multiple-output (MIMO) system with a spatially correlated Rician channel. The correlation between least squares (LS) estimator and its error complicates SE analysis, since signal and interference components become cross-correlated, too. Minimum mean square error (MMSE) estimators do not suffer from this burden. In some previous works, a proper part of the signal is referred to interference, which makes them cross-uncorrelated, and leads to an SE lower bound. In our modified approach, we extract and refer the cross-correlated part of interference to the signal to attain this objective. Here, we use this approach for calculating the instantaneous SE of maximum ratio combining (MRC) detector under LS and MMSE estimation methods. We also derive closed-form approximations of their ergodic SE. This approach is also applicable to other linear channel estimators or data detectors. Numerical results show that achievable SE surpasses that of the previous approach. They also show that our approximation is close enough to Monte Carlo simulation results, especially at the high number of the base station (BS) antennas.