Brokered CD Insurance CD

I've purchased many brokered CD's in my discount brokerage account. The brokerage account is in joint names with rights of survivorship. It also has our 2 adult children as beneficiaries.

A number of the brokered CD's are with the same bank. Does the FDIC insurance limit of $250,000. per person ($500,000 for me and my spouse apply to the total amount of the CD's with the same bank? In this case, I have more than $500,000 in this 1 bank. I thought the brokerage account provides the insurance. Also, I thought having 2 beneficiaries on the joint account increases the FDIC limit.

Please clarify this. Thank you.

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