What are you going to do after school?

Question

1. I am going to go to academy.
2. I am going to go to an academy.
3. I am going to go to the academy.
4. I am going to go to my academy.

5. I am going to go to private institute.
6. I am going to go to a private institute.
7. I am going to go to the private institute.
8. I am going to go to my private institute.

(Which answers are grammatical? Which answers are common ones?)

Answer 1

#3 is grammatically correct
#2 is commonly used
#6 is grammatically correct
#7 is commonly used
I'm almost positive

Answer 2

nautica is correct.

4 and 8 are also correct if the listener knows which academy is yours ... the one you attend.