Nagi is the only heir to the Sanzenin fortune. She isn’t just your average “rich girl.” Calling her “rich” would be selling her short. The “Sanzenin fortune” is so large, throwing away 20 trillion yen in a red herring investment is considered a prank.
Her only surviving family is her grandfather, whom she doesn’t like, so she regards Maria as a mother or older sister figure, and warns Hayate not to touch Maria in any indecent way or she will never forgive him. She has a crush on Hayate, and has misunderstood Hayate thinking that he loves her.