The influence of the interactions between reagents on the excess in the rate coefficient, Deltak, for the instantaneous reaction A+B-->C+B have been investigated by performing large scale molecular dynamics simulations for simple soft spheres. The simulation method has enabled us to determine the contributions to Deltak coming from A-B as well as B-B interactions. The simulations have shown that positive values of Deltak that appear both for the liquid and for the Brownian system [M. Litniewski, J. Chem. Phys. 123, 124506 (2005); 124, 114501 (2006)] result from B-B interactions. If B-B interactions were absent, Deltak was always negative. The influence of B-B interactions was about three times higher for the Brownian system than for the liquid. A qualitative explanation for the effect has been proposed basing on a simple model and analyzing the influence of B-B interactions on fluctuations in concentrations of reagents. The influence of A-B interactions was completely negligible except for the liquid at short times, for which the cancellation of A-B interaction noticeably decreased Deltak.