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How to handle periodic cash reciepts vs. non-periodic accounts payable?

What would be the best manner of handling this senario in LSMB?

A tenant is renting an apartment for $X per month.

The tenant wishes to pay the landlord via. direct deposit from their
paycheck, which arrives every two weeks.

So the tenant calculates a bi-weekly payment amount of ( X*12 ) / 26
to have deposited in the landlord's account each bi-week.

Now, because bi-weeks and month's do not evenly mesh up, some months
the tenant underpays the montly rent, and other months, the tenant overpays
the montly rent, but at the end of a year, the same amount of funds
have changed hands.

What would be the best way to track this in LSMB from the landlord's
point of view?

What I've come up with so far is to make a "customer" entry for the
tenant, and then make an AR transaction on the 1st of each month for
the montly rent (rent is due on the 1st of the month).

What I can't quite deduce is an easy way to enter the cash reciept
from the tenant each bi-week and have it automatically "close" the AR
transactions as time goes by and the bi-weekly reciepts "fill" the
outstanding AR rent transactions.

I tried "spreading" the bi-weekly payment out among outstanding AR
transactions, but eventually I end up with a negative AR payment due
when the tenant is "ahead" of the monthly rent (because I would not
have entered next months AR transaction yet), which then starts to
get either LSMB or me confused and messes up the totals in later

I've also tried simply inputting the bi-weekly payment as a cash
reciept not linked to any particular AR rent transaction.  This works
better in that the totals do not get out of whack in later dates, and
I don't get confused as to what I've done, but then LSMB thinks that
all the AR transactions for the montly rents are "open", even though
in the Outstanding and AR Aging reports it shows no total due.

I do realize I could easily track this with only general ledger
transactions, but then I lose the ability to have the AR outstanding
and AR Aging reports on the inflow/outflow for that customer (or at
least I think I lose that ability).

Does anyone have any ideas/suggestions?

Thanks in advance for any hints.