New measurements with good statistics will make it possible to observe the
time variation of cosmic antiprotons at I AU through the approaching peak o
f solar activity. We report a new computation of the interstellar antiproto
n spectrum expected from collisions between cosmic protons and the interste
llar gas. This spectrum is then used as input to a steady-state drift model
of solar modulation, in order to provide predictions for the antiproton sp
ectrum as well as the antiproton/proton ratio at 1 AU. Our model predicts a
surprisingly large, rapid increase in the antiproton/proton ratio through
the next solar maximum, followed by a large excursion in the ratio during t
he following decade.