The paper deals with the Sparre Andersen model in the collective risk theory. Denote by \(\tau\) the ruin moment; \(\Psi(x,n)= P(\tau(x)\leq n)\) and \(\Psi(x)= P(\tau(x)\leq \infty)\) are, respectively, the probability of ruin before the \(n\)th payoff and in infinite time. Under the hypothesis that the claim sizes are heavy tailed, the author describes the asymptotic behaviour of the difference \(\Psi(x)-\Psi(x,n)\).