Question

Do we need to add subject in the type of letter..?

Answer 1

YES, You need to add it.

Answer 2

Yes It is always recommended to use the formal letters to write the subject. The person at the receiver end will first look for the subject. There by he can easily identity the content inside it all about what.
Writing a subject in a formal letter is a mandate. Just make sure that your subject is crisp and clear which is not more than 6words. Important words or phrases have to be written in the subject.