Time-independent quantum mechanical (TIQM) approach (helicity basis truncated at k = 2) has been used for computing differential and integral cross sections for the exchange reaction H- + D-2 (nu = 0, j = 0-4) -> HD + D- and D- + H-2 (nu = 0, j = 0-3) -> HD + H- in three dimensions on an accurate ab initio potential energy surface. It is shown that the j- weighted differential reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder at four different relative translational energies (E-trans = 0.55, 0.93, 1.16 and 1.48 eV) for (H-, D-2) and at one relative translational energy (E-trans = 0.6 eV) by Haufler et al. for both (H-, D-2) and (D-, H-2) collisions. The j-weighted integral reaction cross section values are in good agreement with the crossed beam measurements by Zimmer and Linder in the Etrans range 0.5-1.5 eV and close to the guided ion beam results by Haufler et al. for (H-, D-2) in the range 0.8-1.2 eV. Time-dependent quantum mechanical (TDQM) results obtained using centrifugal sudden approximation are reported in the form of integral reaction cross section values as a function of Etrans in the range 0.3-3.0 eV for both reactions in three dimensions on the same potential energy surface. The TDQM reaction cross section values decline more sharply than the TIQM results with increase in the initial rotational quantum number (j) for the D-2 molecules in their ground vibrational state (nu = 0) for (H-, D-2) collisions. The computed j-weighted reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder for (H-, D-2) collisions and guided ion beam results by Haufler et al. for both (H-, D2) and (D-, H-2) collisions for energies below the threshold for electron detachment channel.