The term 'eager, informally' can be expressed in two crossword solutions: 'rarin' (5 letters) and 'PSYCHED' (7 letters). Both terms are slang words used to describe someone who is very enthusiastic or excited about something. 'Rarin' is an informal way of saying 'raring to go', which means to be eager and ready to start something. 'PSYCHED' is a more modern term that is used to express enthusiasm and excitement.