Well it is like this about the word thank you (it is hard to translate in such manner)
I thank you - Благодаря ти or (Аз ти благодаря - but that sounds a bit odd and i think is gramaticly incorect)
We thank you - Благодарим ти
thats it for first person.In this case "I" (аз) in the beggining shouldnt be said.
It is a bit hard to explane since this is my native language and i understand it because this is how always was (to my perspective).
Howeever i think we are getting a bit offtopic here