how the capacitor equation can be modified?
When t=0, you get I=I(max) * e^0 
e^0 == 1, because any number to the power of 0 equals 1. 

So you get I_0 = Imax * 1 = Imax = Q/RC = 0.5/(1 * 0.5) = V/R = 1A, of course the current falls as the cap discharges (captured by the e^-t/rc terms as t increases), but at t=0, current is clearly 1A.

I see no problem here.