ShokWaveRider
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You don't have to put it into different institutions if you don't want to. FDIC will cover multiple accounts in the same institution if you title them right. You could put half in your name and half in your spouse's name. Other options include adding a payable on death, joint accounts, etc. A married couple could use various combinations to put well over a million into one institution FDIC insured.
https://www.fdic.gov/deposit/deposits/brochures/your_insured_deposits-english.html
Credit unions. NCUA is better for insurance. Name 3 Beneficiaries and you can get $1.25m Insurance. the CU will advise how to do the title.