It may be of surprise to many but there is actually no biblical,statement that Christ paid for sin.Exactly, Jesus did certainly die as our substitute. And the cross certainly expresses God’s judgment on sin.
But I don't see God the Son became man so that by his suffering and death he could pay the price of sin. This seems to be based on an idea of punishment as a kind of payment, a repayment; the criminal undergoing punishment ‘pays his debt to society’, as we say. It takes a divine man, however, to pay our debt to divine justice.
Now, I can make no literal sense of this idea, whether you apply it to criminals or to Christ. I cannot see how a man in prison is paying a debt to society or paying anything else at all to society. It's punishing a lawbreaker by being locked up in a prison cell.
I think what PSA does is mix up God's Wrath with man's Wrath.
There is vast difference between the wrath of God and the wrath of man. God’s wrath is holy and always justified; man’s is never holy and rarely justified.
The Bible teaches forgiveness not payment though Christ certainly paid a great deal to reconcile us.
Romans 3:21–26 (RSV) — 21 But now the righteousness of God has been manifested apart from law, although the law and the prophets bear witness to it, 22 the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction; 23 since all have sinned and fall short of the glory of God, 24 they are justified by his grace as a gift, through the redemption which is in Christ Jesus, 25 whom God put forward as an expiation by his blood, to be received by faith. This was to show God’s righteousness, because in his divine forbearance he had passed over former sins; 26 it was to prove at the present time that he himself is righteous and that he justifies him who has faith in Jesus.
2 Corinthians 5:18–20 (RSV) — 18 All this is from God, who through Christ reconciled us to himself and gave us the ministry of reconciliation; 19 that is, in Christ God was reconciling the world to himself, not counting their trespasses against them, and entrusting to us the message of reconciliation. 20 So we are ambassadors for Christ, God making his appeal through us. We beseech you on behalf of Christ, be reconciled to God.