Forgiveness of Sins
The Greek word for redeem is "lutroo" meaning to release on receipt of ransom (akin to lutron, a ransom) and is used in the Middle Voice, signifying to release by paying a ransom price (Vines).
The Greek word for forgiveness is "aphesis" and denotes a dismissal, release; it is used of the remission of sins (Vines).
According to Rom. 6:23 "the wages of sin is death." That which we earn (wages) from sin is really a debt that we owe to God. The debt is death (not dying). This death is the wrathful judgment of God poured out as retribution for every sin that is ever committed. Every transgression and disobedience receives a just recompense of reward (Heb. 2:2).
Since God gave the law and God set the penalty for transgression of the law and sin God is Just then every sin must be justly judged and the execution of that judgment carried out. Thus as a result of our sins we were all carrying a huge sin debt (the wrathful judgment of God awaiting to be poured out on the transgressors).
God could not just release us from our sins debt without the payment of that debt. To do so would render God unjust. Since God is Just the debt has to be paid. Thus God cannot just forget about sin and the judgment of sin. Remember all sins must be judged and the wrathful judgment of those sins executed.
Can the sinner pay the sin debt? Of course and he will except someone else pay it. Payment of the sin debt requires an eternal separation from God and the glory of his power and to be cast into the lake of fire of God's vengeance and into the mist of darkness forever. That is not the kind of debt I would care to pay.
Can someone else pay my debt for me? Yes, but he must be without sin and must have been approved of God beforehand to pay the debt. Anyone with their own sin debt cannot pay someone else's sin debt for they have their own debt to settle. Jesus was approved of God, before the world began, in the covenant of redemption to pay the debt of those that God foreknew (Rom. 8:29...30 "for whom he did foreknow...them he also justified). It was said of Jesus by the angel to Joseph that "he shall save his people from their sins." When Jesus went to the cross to pay the ransom price according to II Cor.5:21, "For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him." Thus Jesus at the cross not only took our sins upon himself, but actually became sin for us. During the three hours of darkness Jesus suffered the wrathful judgment of God poured out in execution of our sin debt. The scene was so awful that God turned out the lights (there was darkness over all the earth for three hours). The ransom having been paid Jesus said "It is finished," and bowed the head and gave up the ghost. Thus Jesus through his blood offered himself through the eternal Spirit without spot to God (Heb. 9:14). According to Heb. 10:14 this offering was accepted of God, "For by one offering he hath perfected for ever them that are sanctified." According to Eph. 1:7 this work of redemption and consequent forgiveness of sins was a covenant work for it says that "in whom" (i.e., in Christ) we have redemption..."
In Eph. 1:4 we read, "According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love." Thus God chose us that he might redeem us and make us holy and without blame before him in love.
Also in Eph. 1:7 we are told that this was done "according to the riches of his grace." Grace is defined as unmerited favor. We didn't do anything to earn or warrant or obtain the redemption or forgiveness of sins. We were redeemed and forgiven by the grace of God through the blood redemption of Jesus Christ. This was a complete redemption. In Rom. 8:33, 34 the question is asked and answered, "Who shall lay anything to the charge of God's elect? It is God that justifieth. Who is he that condemneth? It is Christ that died, yea rather, that is risen again, who is even at the right hand of God, who also maketh intercession for us."
Because Christ paid the complete price, no charge can successfully be brought against God's elect. God has justified us, therefore we stand before God in judgment, justified. Praise be to our magnificent and wonderful and gracious God who has loved us even when we were ungodly sinners and has redeemed us by his blood thus forgiving us of our sins.