I know other native speakers will disagree with me but, for me, both "will" and "going to" are fine in both of sentences. Perhaps "will" sounds a little more natural in the first but in the second sentence, they're both fine. You'll probably hear "gong to" more often in BrE when referring to age but that doesn't mean "will" is wrong.
I'm going to be 96 in February.
I'll be 96 in February.