Why do you think Dantes buys de Bouville's investment?

Dumas creates a coincidence where the Inspector of Prisons is the same person to whom M. Morrel owes a considerable sum. This allows Dantes to conveniently both view the prison records and buy Morrel's bank notes from the Inspector. This aids Dantes in confirming that Villefort played a large role in his imprisonment, and it also confirms Caderousse's statements that Morrel tried to help Dantes.

The fact that Dantes purchases the banknotes from Boville, thus becoming a bondholder to whom Morrel owes money is important. As the holder of the banknotes, Dantes becomes the most powerful person in Morrel's life. He can either use these debt notes to help M. Morrel, or to cause him to go entirely bankrupt.