What happens to premium collected when sold put/call is closed...?

Hello,
If I sold (sell to open) a put or call, and then close the trade (buy to close) before expiration, what happens to the premium already credited to me? In other words, what will be my actual profit/loss if I closed the trade before expiration either for a profit or loss? Many thanks

 

Math 101

Premium Collected - Debit Paid - Commissions = Profit/Loss

 

So, sold put 5 contracts and collected $399.57 (500 x $0.81 - comm $5.43) in premium. Decided to buy to close the put 5 contracts at premium $0.88 with comm $5.43, so pay $445.43 (500 x $0.88 + comm $5.43). So my PnL = 399.57 - 445.43 = -$45.86, and i have no further obligations with regards to that contract. Am I correct?

 

Yes ..... Once the trade is closed you have no further obligations.

 

Many thanks