Peter has concluded the body of his letter. He now brings his thoughts to conclusion. He begins by providing a succinct statement as to why he is writing and then a statement of greeting.
I have written briefly to you, exhorting and declaring that this is the true grace of God. Stand firm in it -1 Peter 5:12
I have written on the purpose of 1 Peter while introducing the book (Read it here). Peter places his purpose at the end as the final point to be made to this group of persecuted believers. They are concerned that the persecution they have faced meant that they were outside of God’s favor. They wondered how could someone both be in God’s grace, but at the same time face persecution.