Open Question: Question about a futures price?

That's probably a basic question: If the spot price today is $80 and one month from now a futures contract is priced $81 - does this mean that at expiry both the spot and the futures contract should have the same price? Such as if the spot at expiry is $100 - then the futures contract should be $100? It makes sense, right? Otherwise one can buy the "futures" and sell it for profit or vice versa? 10x