. . Choose which account youd like to transfer money from to your certificate. It's worth noting we've heard banks may move the deceased's savings over to an account with a lower interest rate after they've been told of the account holder's death. Additionally, many banks require you to keep a minimum balance in your savings, and you may pay a penalty fee if you fall below that balance because of making online purchases. PurePoint Financial offers a simple, no fees, no frills, high-interest, online savings account. .