Why Does Faith Save?

Yes, even faith and grace, through which we are today justified, would not of themselves justify us if God’s covenant did not do it. It is precisely for this reason that we are saved: He made a testament and covenant with us that whoever believes and is baptized shall be saved. But in this covenant God is truthful and faithful and keeps what He promised.

Martin Luther commenting on Psalm 51
Luther’s Works v. 10: First Lectures on the Psalms I 236-237