We present 0.9 - 2.5 um resolved spectra for the ultracool binary WISEPC J121756.91+162640.2AB. The system consists of a pair of brown dwarfs that straddles the currently defined T/Y spectral type boundary. We use synthetic spectra generated by model atmospheres that include chloride and sulfide clouds (Morley et al.), the distance to the system (Dupuy & Kraus), and the radius of each component based on evolutionary models (Saumon & Marley) to determine a probable range of physical properties for the binary. The effective temperature of the T8.5 primary is 550 - 600 K, and that of the Y0 - Y0.5 secondary is 450 K. The atmospheres of both components are either free of clouds or have extremely thin cloud layers. We find that the masses of the primary and secondary are 30 and 22 M_Jup, respectively, and that the age of the system is 4 - 8 Gyr. This age is consistent with astrometric measurements (Dupuy & Kraus) that show that the system has kinematics intermediate between those of the thin and thick disks of the Galaxy. An older age is also consistent with an indication by the H - K colors that the system is slightly metal-poor.
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