It's wonderful to see so many positive Hub answers. Mind never grows old; spirit never grows old - love it! Great to see you're still 'On the air' Jewels.
A moment ago I was reading the answer to another Hub in which the writer was convinced that when his body dies everything and every thing ends as far as he is concerned: blackness, void, oblivion, nothing, and no sense of any of this even. Mind you, this did not concern him. Nothing is nothing so what's to worry about.
Semantics always causes concern with these sorts of questions and answers. What some people call soul, I call spirit, for example. What so people call ego is Freud's interpretation, with others it's the Higher Self. But to get to the question.
Bodies do grow old, thinking processes do slow. Recall and absentmindedness commonly become more prevalent, especially if one is not regularly practising ways to delay and slow down such. But that essential spark which is us: the Observer, Witness and Experiencer of our lives does not grow old. It simply IS.
As for the mind - where is the mind? We have what we regard as a personal mind; our learning, memories et cetera. But we have an impersonal mind as well. Our conscious mind might be the iceberg above the water, our impersonal that which lies below. Whilst our Impersonal Mind could well be like the water in which all those icebergs float; perenial, everywhere and at all time.
We humans are caught up with this beginning and end thing, but I'm inclined to believe that is simply because what we observe - and interpret with our reasoning - begins and ends. The All Mighty, God, Nature or whatever we might like to call Her/Him/It might not see things that way at all.