What's the difference between "a year", "per year" and "out of a year"?

Suppose I want to say that I'm at sea seven months out of twelve. (Just an example.)

I think I can say

"I'm at sea 7 months a year"

or

"I'm at sea 7 months per year"

or

"I'm at sea 7 months out of a year"

and in all three cases I would be correct. (Again, I think, feel free to correct me!) But what's the difference? And which one would be the more appropriate?

Solution 1:

7 months a year means 7 months for each/every year.

"Per" in English is used to mean "for each". Therefore 7 months per year = 7 months for each year.

7 months out of a year just comes across as a clumsy way of saying it.