I'm getting started with ClearNow, which does ACH transfers.
With ACH transfers, suppose the transaction is supposed to initiate on Saturday the 15th. It gets delayed to the first business day after the 15th, so in this case, the autodraft won't kick in until Monday the 17th. Then it takes about three days (business days?) to hit my bank account--- so I won't expect to see that until Thursday the 20th. So that's a five-day delay because the date of the original draft didn't fall on a business day.
I had an autodraft on Wednesday the 5th. I wait three days for the funds to be deposited into my account--- but oops, the 8th is a Saturday. So the funds don't actually hit until Monday the 10th, 5 days after the autodraft took place.
So, compared to ACH transfers, which only take place on business days, your P2P can be initiated on any day, even if the funds don't actually make it in the next day. But at least you don't have delays on both sides of the transaction-- just one.
Hopefully, your biz isn't run so close to the line that a weekend's delay throws your budget out of whack. :) It's annoying, but it's bureaucracy.
If you do want your funds to be immediately accessible, you might consider setting up an account at your bank for your tenant to deposit his funds directly into. Then, as long as the deposit is made before 3 pm, it's immediately available. But some banks, like Wells Fargo and Chase, are not allowing non-account-holders to deposit cash into a biz account. So you'd have to see if your bank is willing to provide them with something, like a deposit card, or allow them to deposit a money order, or whatever, to get around your local bank's restrictions.
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