I stand by my opinion that this is deeply disturbing. From a different angle consider the opinions the real people in your life would have. I suppose the real litmus test for this is what would your feelings be if this was reverse. if you had a teenage daughter in a relationship with a 62 year old man would you encourage it? I think too the fact you are questioning this is a big flag for yourself. If your instinct is to even consider the correctness of your actions perhaps that then is an indication of the truth. Remember too that this girl is teenager. I am sorry but I cannot be supportive of this. Besides, you posed this question so it is only fair that multiple points of view be heard.

Protect yourself: emotionally as well as literally. if this is too good to be true, perhaps it isn't. My questioning about this extends to your own well being. What is you are getting in return for your investment in this (not just your time but what may turn out financially too). What is she getting out of this and what is she investing in this.

if this passes the litmus test: you would approve of such an affair with a daughter of your own, you feel comfortable with what friends and family would think, that spending money with no investment on her end is of no consequence; then I suppose we should say good luck and wish you well.