How do I categorize money put in the business by all partners? Can I create an Owner Equity/Drawing account for each partner so I can keep track of each partner's share in the business?
You should set up an equity account for each partner. Example Equity - John Doe. If you are manually entering transactions then any money contributed would be a debit to cash and a credit to the partner that contributed. If importing, then categorize the transactions as Equity - John Doe. Distributions can either go against the same equity account or you can set up a distribution account for each.
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