Why did Egypt establish diplomatic relationship with Israel and did that decision pay off?

As far as I recall, Anwar Sadat was able to convince his people and his followers that establishing diplomatic relationship with Israel will open the door of rapid economic development of Egypt.

My first question is, how did he deduce that ?

My second question is, did we really see that to happen (I guess a big NO)?

And, my third question is, if NOT, why?