Redemption: GREEK-apolutrosis- "to set free, to liberate, to deliver, liberation, deliverance" (Louw-Nida). "to deliver by paying a price" (Scofield).
Regarding justification, this is not a ransom that is paid to Satan in exchange for sinners.
Resources
Romans 3:19-31
The human race belongs to God. He is the Creator, we are the creatures. The ransom paid is due to sin condemning us and enslaving us. "It was God who exacted payment; yet the Bible does not speak of a ransom being paid to God the Father for He did not hold us in bondage" (Radmacher).
Regarding justification, "redemption" is a payment made that sets the believer free from the penalty of sins.
Propitiation: “The Gk. words dealing with the doctrine of propitiation are:
hilasmos, signifying what our Lord became for the sinner (1 John 2:2; 4:10);
*hilasterion*, denoting the place of propitiation (Rom. 3:25; cf. Heb. 9:5); and
hilaskomai, indicating that God has become gracious, or propitious (Luke 18:13; Heb. 2:17).”
TYPE/ANTITYPE- “Types are real persons, events, or things in the Old Testament that have a substantial relationship with corresponding New Testament persons, events, or things. The New Testament fulfilling is called an antitype.”
Sometimes: OT=Physical Events. NT=Spiritual Truths
“Once a year, on the great Day of Atonement, the Jewish high priest and he alone took blood from the great altar of burnt offering and went into the Holy of Holies, into which none dared enter but he and he only for the purpose of this function and sprinkled that blood on the Kapporeth, the cover of the Ark of the Covenant, called the mercy seat, in order to cover the sins of the whole people. In the Ark were deposited the tables of the law, that law which condemned these sins. The Kapporeth covered those tables; but only when it was thus sprinkled with expiatory blood did it cover the sins of the people from God and from his punishment.”
-R. C. H. Lenski, The Interpretation of St. Paul’s Epistle to the Romans, 256.
"Because Christ paid the full ransom price for sin forever and is the Propitiation that satisfied the holiness of our righteous God, God can be righteous while at the same time declaring believers righteous."
-Earl D. Radmacher, Salvation, p. 138
"God is therefore at rest about us forever, however poor our understanding of truth, however weak our walk. God is looking at the blood of Christ, and not at our sins. All claims against us were met when Christ 'made peace by the blood of His cross.'”
-William R. Newell, Romans Verse-by-Verse, 114.