Phonon dispersion relations and vibrational density of states of (Mg_0.9375Fe_0.0625)SiO₃ postperovskite have been determined by direct first-principles calculations of the dynamical matrix up to 150 GPa. Incorporation of iron in the postperovskite phase, irrespective of the two investigated configurations and the spin state, was found to decrease the acoustic phonon frequencies but to have a minor effect on the optic modes at high frequencies. The phonon dispersion curves exhibit negative phonon frequencies below 10 GPa when iron is incorporated in the high or low spin state and indicate unstable dynamic structures. Then, the calculated phonon frequencies of dynamically stable structures are used to determine vibrational contributions to the Helmholtz free energy within the quasi-harmonic approximation. The high temperature equation of state and several thermodynamic properties are then derived for (Mg_0.9375Fe_0.0625)SiO₃ postperovskite and compared with those of pure MgSiO₃ postperovskite. The results show that a low concentration of iron, irrespective of high spin or low spin, in MgSiO₃ postperovskite has a minor effect on the thermodynamic properties at pressure-temperature conditions of the lowermost part of the Earth's mantle.