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The one without soup expressed:
Regarding the above formula, yup, that's correct, providing that you never pay your bill a single day ahead of the due date. If you do, you will be paying less in interest that the amount calculated via the formula. Thanks Yakk for looking that up & typing it out
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Do you happen to know the "continuous" one?
Ie, instead of "interest per period" you have "continuous interest" or "effective annual interest" or "interest compounded instintaniously", and instead of having payments per period you have "payment rate".
It should be easier to play with (more continuous, less discreet), so easier to invert and calculate how payment time changes based on how payment rate changes...
I could do the ODE work. Probably wouild be a good refresher!