Answers to invitations written on visiting cards are always formally worded in the third person, precisely as though the invitation had been engraved.
Invitations In The Second Person
The informal dinner and luncheon invitation is not spaced according to set words on each line, but is written merely in two paragraphs. Example:
Dear Mrs. Smith:
Will you and Mr. Smith dine with us on Thursday, the seventh of January, at eight o'clock?
Hoping so much for the pleasure of seeing you,
Very sincerely,
Caroline Robinson Town.
The Informal Note Of Acceptance Or Regret
Dear Mrs. Town: