Formamidinium lead iodide (FAPbI3) is a newly developed hybrid perovskite that potentially can be used in high-efficiency solution-processed solar cells. Here, the temperature-dependent dynamic optical properties of three types of FAPbI3 perovskite films (fabricated using three different precursor systems) are comparatively studied. The time-resolved photoluminescence (PL) spectra reveal that FAPbI3 films made from the new precursor (a mixture of formamidinium iodide and hydrogen lead triiodide) exhibit the longest lifetime of 439 ns at room temperature, suggesting a lower number of defects and lower non-radiative recombination losses compared with FAPbI3 obtained from the other two precursors. From the temperature-dependent PL spectra, a phase transition in the films is clearly observed. Meanwhile, exciton-binding energies of 8.1 and 18 meV for the high- and low-temperature phases are extracted, respectively. Importantly, the PL spectra for all of the samples show a single peak at room temperature, whereas at liquid-helium temperature the emission features two peaks: one in higher energy displaying a fast decay (0.5 ns) and a second red-shifted peak with a decay of up to several microseconds. These two emissions, separated by ~18 meV, are attributed to free excitons and bound excitons with singlet and triplet characters, respectively.