Formally: "I regret that I shall not be able to complete my assignment on time, but I will do my best to finish by the following morning."
Informally: " I am sorry. I can't finish the assignment on time, but I'll do what I can to get it to you the next day".
The first puts a distance between you and the recipient; the second implies a closer relationship. I would advise being sure the teacher will be happy about informal approaches.