It costs $41,000 a year for a foreign student to study in the U.S. And it takes at least two years to complete the graduate study.
==> 'the' sounds odd in that context. Try,
to complete graduate studies.
to complete the graduate studies programme. ("the" as in "our school's")
to complete the graduate course of study. ("the" as in specific kind of course of study)
to complete a graduate studies degree. ("a" means, any graduate degree)
He is entertaining the idea of working for her after his current assignment has ended in December 2004. (Present Perfect: after...has ended)