Romance manga where a guy tutors a girl who turns out to be a millionaire
I am sure the manga in question is Billionaire Girl

The guy's name is Takato Kei. He tutors this rich teenage girl for 10000 Yen per hour.



It a complete romance story. In reality she is not a high school girl who has amassed a lot of wealth from stock market. I think this covers the description you gave. Hope this helps :D

BTW Fun-Fact: I just noticed it was written by Isuna Hasekura (of Spice and Wolf fame :D ).