"저는 당신을 아주 사랑합니다." It is grammatically correct but to me this sentence looks like the written sentence in a letter or proposal in a public place. Or you can find this sentence as lines in a old movie or a play. Usually, when young Korean couples confess or talk about their love, it is more often that they talk in informal way. For example, 너를 정말 사랑해. (I love you so much.)

My link seemed to have disappeared?? http:// www.allkpop.com/article/2015/03/footage-containing-the-argument-between-lee-tae-im-and-yewon-revealed-shows-yewon-speaking-informally take away the space

Yes in korean if you said something informal to someone you are not close with or some you respect or are older than you, it would be interpreted as very rude. And if you said something formal to someone you're close with or who's clearly younger than you, that would either be strange or extremely polite. Like once I'm not sure if you knew there was a k-celeb that spoke informally and rudely to an older person, which got her in so much trouble and hate from people. She was labelled rude and very disrespectful. <http://www.allkpop.com/article/2015/03/footage-containing-the-argument-between-lee-tae-im-and-yewon-revealed-shows-yewon-speaking-informally>

That sparks another question! If you did say the formal way to an intimate person would they be greatly offended?

Oh ahaha well I meant to help you! Because this seems like something you'd say to someone you were more intimate and therefore it will be way more casual (예) 반말)