Boolean AND not giving correct decision. TODAY() and NOW() involved

I am trying to create a formula that displays a cell date if today’s date is greater than or equal to a “parameter” date, and the time now is greater than or equal to a “parameter” time. I have checked the system format and the LibreOffice Calc format but I am getting a value from NOW() that is not correct.

This is my formula;

=IF(AND(TODAY()>=$Rates.$B8,(TODAY()-NOW())>=$Rates.$B7),$Rates.$B8,“Before Bell”)

$Rates.$B8 is the target date to which the current date has to be greater than or equal.
$Rates.$B7 is the target time to which the current time needs to be greater then or equal.

I don’t seem to be able to post an image of the function wizard, but basically the values displayed in the wizard seem to show the expected values, and therefore the result should be TRUE (THEN), but the returned value is the FALSE (ELSE) value.

I cannot see the fault. Can someone spot it for me.

Today() is midnight, when Today began. Now() is also Today plus a few hours-minutes-seconds since midnight. In other words, Now() is almost always slightly greater than Today(). Just subtract Today() from Now(), not the other way around.
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That makes so much more sense!!!

I did get my solution from an internet post. I’ll just have to think about things more.

Thanks you so much.

Grace