  The measurement of the charge asymmetry $A_{FB}(e^-e^+\to \mu^-\mu^+)$ will
play an important role at the high-luminosity circular electron-positron
collider FCCee considered for construction at CERN. In particular, near the Z
resonance, $\sqrt{s} \simeq M_Z \pm 3.5$ GeV, $A_{FB}$ will provide a very
precise value of the pure electromagnetic coupling constant
$\alpha_{QED}(M_Z)$, which is vitally important for overall tests of the
Standard Model. For this purpose, $A_{FB}$ will be measured at the FCCee with
an experimental error better than $\delta A_{FB} \simeq 3\cdot 10^{-5},$ at
least a factor 100 more precisely than at past LEP experiments! The important
question is whether the effect of interference between photon emission in the
initial and final state can be removed from the $A_{FB}$ data at the same
precision level using perturbative QED calculations. A first quantitative study
of this problem is presented here, with the help of the KKMC program and a
newly developed calculation based on soft photon resummation, matched with NLO
and NNLO fixed-order calculations. It is concluded that a factor of 10
improvement with respect to the LEP era is obtained. We also present a clear
indication that reducing the uncertainty of charge asymmetry near the Z peak
due to IFI down to $\delta A_{FB} \simeq 3\cdot 10^{-5}$, i.e. the expected
experimental precision at FCCee, is feasible.
