[Background] Alpha-nucleus optical potentials are basic ingredients of statistical model calculations used in nucleosynthesis simulations. While the nucleon+nucleus optical potential is fairly well known, for the alpha+nucleus optical potential several different parameter sets exist and large deviations, reaching sometimes even an order of magnitude, are found between the cross section predictions calculated using different parameter sets. [Purpose] A measurement of the radiative alpha-capture and the alpha-induced reaction cross sections on the nucleus 115In at low energies allows a stringent test of statistical model predictions. Since experimental data is scarce in this mass region, this measurement can be an important input to test the global applicability of alpha+nucleus optical model potentials and further ingredients of the statistical model. [Methods] The reaction cross sections were measured by means of the activation method. The produced activities were determined by off-line detection of the gamma-rays and characteristic x-rays emitted during the electron capture decay of the produced Sb isotopes. The 115In(alpha,gamma)119Sb and 115In(alpha,n)118Sbm reaction cross sections were measured between Ec.m. = 8.83 MeV - 15.58 MeV, and the 115In(alpha,n)118Sbg reaction was studied between Ec.m. = 11.10 MeV - 15.58 MeV. The theoretical analysis was performed within the statistical model.