This study examines user acceptance of AI technologies in financial services to promote inclusive and user-centered AI design. By analyzing perceived usefulness and adoption intention, it compares users with and without prior experience in using financial AI services. Using survey data from 6352 Korean adults from the 2023 Digital Divide Survey (conducted by the National Information Society Agency of Korea), the study addresses two research questions: (1) What factors influence the perceived usefulness of financial AI services among users with and without prior experience? (2) What factors influence the adoption intentions of financial AI services among users with and without prior experience? Findings reveal that for perceived usefulness, users with prior experience benefit from positive AI perceptions and both bonding and bridging social capital. Among users without prior experience, positive AI perceptions, digital self-efficacy, and bonding social capital are significant predictors, while bridging social capital is not. Logistic regression results reveal contrasting adoption determinants. For users with prior experience, positive AI perceptions and bridging social capital significantly influence adoption, with the latter having a negative effect. In contrast, for users without prior experience, positive AI perceptions and both bonding and bridging social capital are critical. These findings highlight the role of user experience in shaping attitudes and intentions, emphasizing the need for tailored strategies in human-computer interaction. Experienced users benefit from social networks and targeted information, while users without experience require self-efficacy support and reduced perceived barriers. This study contributes to the design of inclusive AI-driven financial systems by addressing diverse user needs and fostering broader AI adoption.