Moneydance's open source API and GnuCash are examples, but you will find many more open source software titles from Heather Johnson, who covers Free Geekery for RewardPrograms.org. Heather has compiled a list of 50 Awesome Open Source Financial Tools for personal and small business finance, investing and financial calculations.
I have not tested the software listed myself, but I recommend checking it out. If you download any of the listed the software, scan it with your anti-virus software before installing, which is what I do for all downloaded software.
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