The fact that Arsenal has been shifting the bid to accommodate Rice after many rejections from West Ham proves that they really needed him and the initial price trades was just market thing, they needed him that's why they had agreed on the $105M and what I think could have push Arsenal for that amount was because Manchester City were also on the raise but pulled out as soon as Arsenal presented another and when they think it's out of their financial plans, they let Arsenal have the deal and it's now theirs to buy.
How will Declan proves depends on next season, nobody can say this is exactly what he is going to do but since his past is good, I expect him to perform well in Arsenal if they put him in good use, and I think if he do well by next season, it's another opportunity for him to increase his transfer fee to another club and so does his market value.
Declan Rice is a statement signing from Arsenal and Arteta and it could be the final push that the team needs to finally win the Premier League this coming season. I also expect Rice to perform excellently well, especially as he is going to play with Odegaard and Trossard in midfield. Its a promising season ahead for Arsenal.