We write this to make our joy complete.
Here is the second reason for the writing of this book: complete joy.
In the NIV Bible, there is a text not that states that the word our is the word your in some manuscripts. I think that this is interesting because both seem to work.
Understanding the message of the gospel will bring complete joy for the one who hears the call and responds to it. But it can also bring joy to the bearer of the message. There is probably no greater joy than to be a carrier of God's good news.
The real question to ask though is, "Do you have complete joy?"
And if you do not, "why?"
...both important questions to ask.