Humans systematically make poor financial judgments, a problem that can be mitigated with advice, whether it be from humans or, increasingly, artificial intelligence (AI). Yet, one potential obstacle in human-AI interaction is algorithm aversion, where people prefer humans over AI advisors. However, whether this preference affects the integration of advice remains unclear. We investigate AI advice integration in financial judgements and its underlying psychological drivers. In two studies, participants (N=716) engaged in incentivised investments, receiving AI or human advice. Results showed that participants integrated AI and human advice similarly, even if they preferred human advice. However, those with strong preferences integrated information better from their preferred source. We further find that different psychological factors impact preferences and advice integration, suggesting that advice preference and advice integration are independent of each other. These findings highlight the potential for AI to enhance financial judgements, even among individuals averse to its use.