The approximation of the individual risk model by a compound Poisson model plays an important role in computational risk theory. It is thus desirable to have sharp lower and upper bounds for the error resulting from this approximation if the aggregate claims distribution, related probabilities or stop-loss premiums are calculated. The aim of this paper is to unify the ideas and to extend to a more general setting the work done in this connection by BOHLMANN et al. (1977), GERBER (1984) and others. The quality of the presented bounds is discussed and a comparison with the results of HIPP (1985) and HIPP & MICHEL (1990) is made.