I'm not sure about what you are looking for exactly, but based on what you've given us so far, I can see a possible approach of adding your members as 'customers' and issuing an 'invoice' to them for 'shares'. You can then obtain a Customer Report which is essentially a Statement of Account. There is an option to turn on linked document detail so you can see which payments applied to which invoices.

As for tracking their level of equity, that's a whole other ball of wax. While the invoicing system might allow you to include equity accounts, I don't know of a way to restrict this on a 'cash basis', that is, their equity isn't what they've promised to pay, but what they've actually paid. (The Business Features are designed for Accrual Accounting)

I suspect if that is your need, you'd skip the invoicing/customer system (Business Features) and just do your transactions manually.

You'd need AR sub-accounts for each member most likely.

And as others have noted, once you figure out how to do what you need via pen and paper, we can better assist with doing the same with GnuCash if you can't manage to see the solution right-off.

Regards,
Adrien

On 8/1/23 1:26 AM, gibel...@gmx.net wrote:
And yet, apart from that, it would already help me a lot if there was an
idea how I could promptly and internally (i.e. without all tax aspects
and legal requirements) map the (partial) payments of members and their
shares in the overall project, because the other tasks will take up
quite a bit of time, I fear.

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