Neutrinoless double-β (0νββ) decay is a promising beyond standard model process. Two-neutrino double-β (2νββ) decay is an associated process that is allowed by the standard model, and it was observed in about 10 isotopes, including decays to the excited states of the daughter. Sn124 was the first isotope whose double-β decay modes were investigated experimentally, and despite few other recent efforts, no signal has been seen so far. Shell model calculations were able to make reliable predictions for 2νββ decay half-lives. Here we use shell model calculations to predict the 2νββ decay half-life of Sn124. Our results are quite different from the existing quasiparticle random-phase approximation results, and we envision that they will be useful for guiding future experiments. We also present shell model nuclear matrix elements for two potentially competing mechanisms to the 0νββ decay of Sn124.