Do short puts create a margin loan?

Let's say a trader has $10K on his account. With that he can buy 200 shares of XYZ stock at $100/share ($20K total). If he does that, he will have a margin loan of $10K on which he will pay margin interest. Now, let's say that our trader sold 2 100 XYZ puts for $200 each. He now has $10400 cash, but how much buying power does he still have? $400 or zero? Is the additional cash required to purchase XYZ stock ($9600) in case the puts get assigned considered a margin loan and is a subject to margin interest?