Funny you should ask this question. This week I am starting with a new student who is 85 years old…

The only real limitation to learning is death. So get on with it!

As for grades, the usual consensus seems to be that it takes around one year to complete a grade. So for grade 4 we are talking 4 – 5 years. (The ABRSM actually says it in their website).
This is of course rubbish. Although time is always dependent on the student (how much time and effort s/he is prepared to dedicate to the instrument) and his/her talent (how fast s/he learns, how naturally co-ordinated s/he is, etc.), on the environment and on the teacher, I see no reason why it should take that long. In fact I have successfully and consistently brought students to grade 8 level in 2 – 3 years.
As one example (not at all exceptional), one of my students is in her sixties, has mild arthritis and after one year of lessons (just completed in September) can play amongst other pieces, Schubert’s Impromptu op. 142 no. 2, Satie’s Gymnopedies 1, 2 and 3, Chopin preludes 4, 7 and 20, Bach 2 voice inventions no. 1 and 9, Joplin’s Pineapple Rag, Scarlatti sonatas K32, and K 213. We are now working on Chopin’s Etude Op. 25 no. 1, Schubert’s Impromptu op. 90 no. 3 and Mozart “Ah Je vous Dirais Maman” variations.
However, I must say that you do not usually get this sort of results with the "normal" weekly 30 minute lesson.
Good luck with your piano studies,
Best wishes,
Bernhard.