This article is from the ER FAQ, by Rose Cooper email@example.com with numerous contributions by others.
In the episode "Love Among the Ruins" , it's revealed
that Carter's father is one of the wealthiest men in Chicago, worth
$178 million. (In that episode, a rich patron of the hospital who
recently paid for a new cardiac wing discovers that his son and
Carter went to prep school together.) Carter's wealthy background
isn't brought up much [make that, wasn't...until the fourth season,
in the "How To Get That Anna Chick All Hot And Bothered" arc], but
it's fairly evident that he doesn't have a problem affording things,
unlike the heavily-indebted residents.
...of course, "wealthy" is relative </bad pun>: Gamma Carter, in
retaliation for Carter not being fully up-front about Chase's drug
addiction (which she believes, in turn, "caused" Chase's overdose), took
away Carter's Trust Fund in "Gut Reaction" , with the Ensued Hijinx
beginning in "Shades of Gray" . Poor Little Rich Boy...