How to deny the usage of my product to a user?

I am building an microcredit application that is checking for the user's eligibility.

Unfortunately not everyone is eligible, I have to announce it and it can generate some frustration. I would like to smoothen this experience as much as possible.

How can I write a message to inform the user that I cannot provide him access to my product and leave him on a rather positive note if possible?

Specifically:

  • Should I apologize? (there is already a good response about apologizing for error messages here: https://ux.stackexchange.com/a/31362/112906)
  • Should I try to explain the rationale behind? It can be quite complex and some part of the decision-making process cannot be communicated.
  • Can I use visual elements or specific colors to improve this experience?
  • Should I leave him with this last screen or propose some additional actions ? (eg a button to leave the app, propose him to leave some feedback, etc...)
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