Right age for PhD or should I just rely on my MFin?

Hello, new chimp here. Hope you're all doing well. I just wanted to ask few questions regarding PhD(they're general). 1) What is the most appropriate age for applying to PhD(I'm looking at CalTech, Princeton, & University of Chicago)? 2) I'm 24 and let's say I apply to Caltech's PhD in Math & Computing next year(I'll be 25), do you think I'll be too old for PhD? I went to MIT(1 year MFin which is much more quantitative than my undergrad in management) and because my undergrad is not that quanty, so I had to go for 1 year quantitative program to "rebrand" myself for PhD(my profile was weak because it lacked quantitative skills/background before MIT). I am a risk analyst at a BB

I love financial engineering and I love math and computing. There are 2 reasons for wanting PhD. 1) I just love math/stat/computing(I discovered that in my undergrad and realized that I had made a great mistake but it's done now and I had to make things right). Second reason is because I personally think that with MFin or all the MFEs, you reach a point in your career where it becomes dormant. You don't have enough qualifications to move beyond that point because I've heard(never seen) that hardcore finance positions require PhDs in highly quantitative subjects.And I want to work in hedge funds as a quant. Illiprogrammer, please enlighten me if I'm wrong. I just have that impression that one cannot go far in their career with MFin.