Notice in Psalms 105 and 106 how the exodus story is retold... once again. This was the defining moment in the life of Israel. 105 tells the story of the exodus itself. 106 tells of Israel's disobedience in the wilderness and the Promised Land.
Could this have been written to a nation in exile? Israel in Babylon? It is likely that the story of the exodus was a favorite of those Jews relocated to the land of Persia. It would have been a natural way for a disenfranchised people to remind themselves that their God had delivered them before, and could deliver them again.
On the other hand, Psalm 106 recounts the nation's unfaithfulness to God who had delivered them from Egypt. Could this perhaps be a warning to not make the same mistake once they were delivered from the Persians? The lesson: God freed our fathers from Egypt, but they soon forgot to be thankful. When God frees us from Babylon, let's not make the same mistake.
Have you ever said, only to be sorry later, "Oh, that could never happen to me?"