Great question, danyielg. Reg CC can be quite confusing as there are many complicated parts to the rules.
As Randy said, they should not have used the "reasonable cause to doubt collectability" reason as not being able to verify funds (when a bank won't provide this information to you) is not a valid reason. In order to use this reason, they would have had to have received some information from the other bank, such as a statement that the check would not be paid. The fact that you were not able to verify funds is not a sufficient reason to hold funds.
That said, they can absolutely use the large deposit exception hold. Unless their funds availability disclosure says they will give the customer availability on the same day as the deposit, Reg CC permits them to provide availability of the first $5,525 on the next day and the remaining balance on the seventh business day.
So, here is what you should have done for your $20,000 check: $5,525 available on the next day and $14,475 available on the seventh day after the day of deposit - using only the large deposit exception hold.
Now, as a clarification, seventh day availability (instead of just six days) is permitted for some next day items (i.e. your cashier's check) for special exception holds, based on the commentary which says:
3. With respect to Treasury checks, U.S. Postal Service money orders, checks drawn on Federal Reserve Banks or Federal Home Loan Banks, state and local government checks, cashier's checks, certified checks, and teller's checks subject to the next-day (or second-day) availability requirement, the depository bank may extend the time funds must be made available for withdrawal under the large deposit, redeposited check, repeated overdraft, or reasonable cause exception by a reasonable period beyond the delay that would have been permitted under the regulation had the checks not been subject to the next-day (or second-day) availability requirement. The additional hold is added to the local or nonlocal schedule that would apply based on the location of the paying bank.
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Adam Witmer, CRCM
All statements are my opinion, not those of my employer, and should not be taken as legal advice.
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