It will be worth one dollar unless it is gaining interest or it is some kind of misprint making it more valuable. I have a couple of dollar bills that I thought might be worth something since they are dated 1935 and 1932, turns out that they are only worth about $1.50 each. It was rather disappointing to say the least!
Nowadays you have to show a little action on your account like every 3 or 5 yrs or the bank will close your account and take your money. So I say if you put a dollar in the bank and just leave it, in 35 yrs it will be worth 0 and you won't have an account anymore.