  We develop a new method to account for the finite lifetimes of stars and
trace individual abundances within a semi-analytic model of galaxy formation.
At variance with previous methods, based on the storage of the (binned) past
star formation history of model galaxies, our method projects the information
about the metals produced by each simple stellar population (SSP) in the
future. Using this approach, an accurate accounting of the timings and
properties of the individual SSPs composing model galaxies is possible. We
analyse the dependence of our chemical model on various ingredients, and apply
it to six simulated haloes of roughly Milky Way mass and with no massive close
neighbour at z=0. For all models considered, the [Fe/H] distributions of the
stars in the disc component are in good agreement with Milky Way data, while
for the spheroid component (whose formation we model only through mergers)
these are offset low with respect to observational measurements for the Milky
Way bulge. This is a consequence of narrow star formation histories, with
relatively low rates of star formation. The slow recycling of gas and energy
from supernovae in our chemical model has important consequences on the
predicted star formation rates, which are systematically lower than the
corresponding rates in the same physical model but with an instantaneous
recycling approximation. The halo that resembles most our Galaxy in terms of
its global properties also reproduces the observed relation between the average
metallicity and luminosity of the Milky Way satellites, albeit with a slightly
steeper slope.
