Still wrestling with Romans (and always will be!), how’s this sound for a description of the purpose of Romans:
In my estimation, the reason for Romans are multiple and complex. Paul writes to the Roman churches, primarily to the Gentiles, but knowing full well that Jewish Christians in the city will hear about the letter, perhaps even from his delegate Phoebe (Rom 16:1-2). Paul wants the financial support of the Roman Gentiles for his planned journey to Spain and as he prepares to return to Jerusalem to deliver the collection with all of the Gentile churches firmly behind him as the Apostle to the Gentiles (Rom 15:24-25). In order to win their financial favor and willingness to voluntarily come under his apostolate, Paul has two implied tasks. First, he must win them over to his version of the gospel (Rom 1:9, 15-16; 15:15-21). He does that by setting out his gospel at theological depth in order to better “establish” them (Rom 1:16; 16:25). He appeals to shared traditions (e.g., Rom 1:3-4, 3:22-25; 4:25; 15:15) and makes apologetic remarks where necessary to assure them that he is not antinomian or anti-Israel, but is a kosher advocate of the Jewish Christian gospel about Israel’s Messiah (Rom 3:8; 6:1-2; 9:1-5). Paul’s strength is that he is able to provide sophisticated scriptural and rhetorical arguments explaining how God through the Messiah welcomes Gentiles into the family of Abraham, and how Jews and Gentiles in the Messiah should equally welcome one another (Rom 4:16; 5:8-11; 15:6-7). Paul, in effect, gospelizes them, by which I mean that he endeavors to conform them to the evangelic character of his vision for Christian communities. Paul wants to make the Romans a pristine example of a “faithful obedience” among the Gentiles (Rom 1:5; 16:26) that his opponents believed that his converts lacked. Since Paul cannot be there in person to impart a spiritual gift to them, to reap a full harvest by preaching the gospel in Rome, he does the next best thing. He imparts to them the blessing of his gospel, hoping that it will place them in his debt, a debt that will be repaid when he arrives in Rome. This way we account for the themes of apostleship, Gentiles, gospel, mission, Rome, and Spain, that are so prominent at the beginning and end of the letter. A second implied task is some preventive pastoral care. Paul knows the dangers that the churches in Rome face. The possibility of anti-Paulinists arriving in Rome (Rom 16:17-18), the fragmentation of the house churches over Torah and Halakhah perhaps exacerbated by the departure and return of Jewish Christians to Rome (Romans 14), the need of strategy for negotiating the perils of living in a pagan society (Romans 12–13), preemptively countering the possibility of Gentile Christians imitating the rancorous anti-semitism of Roman cultural elites (Romans 9, 11), affirming the interlocking nature of Jewish and Gentile missions (Rom 1:16; 10:14-21; 11:13-33; 15:8-9, 27), demonstrating a way of explaining to Jewish neighbors a messianic theodicy for the existence of evil (Rom 8:18-39; 16:20), and expositing God’s faithfulness to Israel and his impartiality towards Jews and Greeks in Jesus Christ concerning judgment and justification (Romans 1–4, 9–10, 14:9-10). In sum, Romans is a word of exhortation, a masterpiece of apologetics, missionary theology, christological exegesis, pastoral care, theological exposition, and artful rhetoric – all designed to win over the audience to Paul’s gospel, to support his mission in Spain, to draw Jewish and Gentile Christians in Rome closer together, and for his audience identify with the Apostle to the Gentiles as he goes to Jerusalem.
 David E. Aune, “Romans as a Logos Protreptikos,” in The Romans Debate, ed. K.P. Donfried (Peabody, MA: Hendrickson, 1991), 278-96.