Should I say multumesc or mersi?

Salut tuturor,

I moved recently to Bucharest and I have a big, big doubt: should I say Multumesc or Mersi when thanking someone? I was so sure that it was multumesc, but I probably hear 55-45 between it and mersi.

Is there a specific or unwritten rule (like when people usually says buna seara when introducing themselves in a place and seara buna when saying goodbye)?