I am not clear about putting a full stop after yout initials when signing a formal letter.
Should it be: yours sincerely, P. Simpson or P Simpson (without the full stop) ?
I occasionally see the latter in modern textbooks.
There is an increasing habit of omitting full stops after initials in names. If you want to use them, do so. It is neither wrong nor right, but whatever you prefer. Personally I prefer them.