Romans 13:8 — Owe no man any thing, but to love one another: for he that loveth another hath fulfilled the law.
This verse is tied to the beginning of verse 7, but over and above.
It's not referring to money specifically (although we shouldn't take on obligations we can't repay). I am debtor both to the Greeks, and to the Barbarians; both to the wise, and to the unwise (Romans 1:14).
Paul sets forth Christian duty in two distinct realms. In 12:4 he shows that every member is set in his proper place in the church. So first there is the Christian's duty in the realm of the church. Then, in the thirteenth chapter, Paul shows the Christian's duty in the realm of the state. The Christian's duty in the church and in the state should be enforced and performed in just one way, in love. — Alva J. McClain, Romans: The Gospel of God's Grace, page 219.
We are redeemed from the curse of the law (Galatians 3:13), that the righteousness of the law might be fulfilled in us (Romans 8:4).
But why bring the Law in? Does not Galatians 3:13 declare that Christ hath redeemed us from the curse of the law, being made a curse for us? Yes, but Romans 8:4 explains that He has done this that the righteousness of the law might be fulfilled in us who walk not after the flesh, but after the Spirit. In Galatians 5:14, again referring to the manward side of the Law, the apostle says: All the law is fulfilled in one word, even in this, Thou shalt love thy neighbor as thyself.
Thus he concludes in Romans 13:10: Love worketh no ill to his neighbor; therefore love is the fulfilling of the law. How true! The Law is a testimony to human depravity (1 Timothy 1:9-10). If all men loved each other what ned would there be for laws? It is a blessed reality, then, that as we are saved and disciplined by grace: the love of God is shed abroad in our hearts by the Holy Ghost which is given unto us (Romans 5:5).
While not under the covenant of the Law then, the believer under grace may nevertheless fulfill all the statutes of the Law regarding mans' behavior to his neighbor by simply letting the love of God motivate him. — C.R. Stam, The Epistle of Paul to the Romans, page 316.