ATM ^ ATF European calls, briefly

Refer to my simplified BS formula in http://bigblog.tanbin.com/2011/06/my-simplified-form-of-bs.html.

Q: for a ATF European call, where K == S*exp(rt) i.e. struck slightly Above current spot, how would the BS formulas be simplified
d1 = -d2 = 0.5σt  =   …………………. (in more visual form)

C(S,t) = S * [ N(d1) – N(-d1) ] = S * [2N(d1)-1] and depends only on sigma scaled Up for 2.5 years (our t)

Q: how about an ATM European call, where S==K?
A: the ATM call (slightly Lower strike than ATF) has more moneyness than the ATF call , because stock will drift past K long before expiry. The diffusion of the stock prices is “centered” around the drift.