Jesus equated sin with debt. He did it in the different versions of a very famous prayer that is found in two versions and to the Gospels:  Matthew and Luke.

Matthew 6:9-13
9 “Pray, then, in this way: ‘Our Father who is in heaven, Hallowed be Your name.
10 ‘Your kingdom come. Your will be done, on earth as it is in heaven.
11 ‘Give us this day our daily bread.
12 ‘And forgive us our debts, as we also have forgiven our debtors.
13 ‘And do not lead us into temptation, but deliver us from evil. For Yours is the kingdom and the power and the glory forever. Amen.’

And…

 Luke 11:2-4
2 “And He said to them, “When you pray, say: ‘Father, hallowed be Your name. Your kingdom come.
3 ‘Give us each day our daily bread.
4 ‘And forgive us our sins, For we ourselves also forgive everyone who is indebted to us. And lead us not into temptation.’ ”

In Matthew 6:12, the word for “debt” is ὀφείλημα, opheilama and it means…

• “literally, what is owed debt, sum owed; in a broader sense of what is due obligation”¹Friberg, Timothy, Barbara Friberg, and Neva F. Miller. Analytical Lexicon of the Greek New Testament. Baker’s Greek New Testament Library. Grand Rapids, MI: Baker Books, 2000.
• “OPHEILĒMA (ὀφείλημα , (3783)), a longer form of No. 1, expressing a debt more concretely, is used (a) literally, of that which is legally due, Rom. 4:4; (b) metaphorically, of sin as a debt, because it demands expiation, and thus payment by way of punishment, Matt. 6:12.”²Vine, W.E., and F.F. Bruce. Vine’s Expository Dictionary of Old and New Testament Words. Old Tappan NJ: Revell, 1981.

In Luke 11:4, the word for “sin” is ἁμαρτία, hamartia and it means…

• “ἁμαρτία, ας, ἡ sin; (1) of an act, a departure from doing what is right, equivalent to ἁμάρτημα sin, wrongdoing (1J 5.17); (2) as the moral consequence of having done something wrong sin, guilt (AC 3.19; 1J 1.7); (3) as the nature of wrongdoing viewed as the rejection of God by self-assertive human beings sin, evil (RO 5.12, 13; cf. 1.21).”³Friberg, Timothy, Barbara Friberg, and Neva F. Miller. Analytical Lexicon of the Greek New Testament. Baker’s Greek New Testament Library. Grand Rapids, MI: Baker Books, 2000.
• “ἁμαρτία [hamartia /ham·ar·tee·ah/] n f. From 264; TDNT 1:267; TDNTA 44; GK 281; 174 occurrences; AV translates as “sin” 172 times, “sinful” once, and “offense” once. 1 equivalent to 264. 1A to be without a share in. 1B to miss the mark. 1C to err, be mistaken. 1D to miss or wander from the path of uprightness and honour, to do or go wrong. 1E to wander from the law of God, violate God’s law, sin. 2 that which is done wrong, sin, an offence, a violation of the divine law in thought or in act. 3 collectively, the complex or aggregate of sins committed either by a single person or by many.”⁴Strong, James. Enhanced Strong’s Lexicon. Bellingham, WA: Logos Bible Software, 2001.

Sin is breaking the law of God.

• “Everyone who practices sin also practices lawlessness; and sin is lawlessness,” (1 John 3:4).

So, since sin is breaking the law, sin is a legal problem. It is a legal debt. But praise be to God in the person of Christ who paid our sin debt on the cross.

• “having canceled out the certificate of debt consisting of decrees against us, which was hostile to us; and He has taken it out of the way, having nailed it to the cross,” (Colossians 2:14).
• “and He Himself bore our sins in His body on the cross, so that we might die to sin and live to righteousness; for by His wounds you were healed,” (1 Peter 2:24).

All who trust in what Christ did on the cross, will be cleansed of their sins by faith what Christ has done.

• “What then shall we say that Abraham, our forefather according to the flesh, has found? 2 For if Abraham was justified by works, he has something to boast about, but not before God. 3 For what does the Scripture say? “ABRAHAM BELIEVED GOD, AND IT WAS CREDITED TO HIM AS RIGHTEOUSNESS.” 4 Now to the one who works, his wage is not credited as a favor, but as what is due. 5 But to the one who does not work, but believes in Him who justifies the ungodly, his faith is credited as righteousness,” (Romans 4:1-5).