Is it permissible to abort a fetus that is four weeks old due to the impact of pregnancy on the wife, the husband's studies, and his expenses and medical treatment?

It is not permissible for a woman to abort what is in her womb—even if it is merely a drop of fluid into which the soul has not yet been breathed, or whose creation has not yet been completed—except out of necessity. What was mentioned in the question is not a necessity. Allah has guaranteed the sustenance of children. Allah Almighty says: "And do not kill your children for fear of poverty. We provide for them and for you. Indeed, their killing is ever a great sin." And Allah Almighty says: "And do not kill your children for fear of poverty. We provide for you and for them."