Depreciating Value by Month

Was there a typo here?

If a user selects the Depreciation Start Date to be June 28th, 2018, then on June 1st, 2018the Remaining deprecation value will be adjusted. 

Try this.  The purpose of defining today as a fixed date is to be able to try different values for total to test the formula.

var date Today = Date(2019,1,15);

var date EffectiveStart = FirstDayOfMonth([Start Depreciation]);
var date EffectiveToday = FirstDayOfMonth($Today);

var date ES = $EffectiveStart;
var date ET = $EffectiveToday;

var number MonthsStepOne = (Year($ET) - Year($ES)) * 12;

var number MonthAdjustment = If(Month($ET) >= Month($ES), Month($ET) - Month($ES) +1,  // both ends count as a month, so add 1
     (Month($ET) - Month($ES)) + 1);
   
var number Months = $MonthsStepOne + $MonthAdjustment;

Max(0, [Original Amount] - [Original Amount]/[Depreciation Term (months)] * $Months)

This got me close but it didn't output the number i was hoping.  I have an item with Original Ammoun = $100 and Deprecation Term (months) = 36.  The Start Deprecation = July 1.  But the formula is outputting a value of $80.55. The actual value should be $97.23 ($100 - $2.77). 

Maybe i'm misunderstanding what you meant by "The purpose of defining today as a fixed date is to be able to try different values for total to test the formula.

It seems that the var date Today needs to equal the date (first day of the month) that this formula should identify.

Once you feel that the logic is working for a day of your choice, you would set that line to read

var date Today = Today();

I did it that way to have a way to test my logic as while I am all powerful, I cannot yet  actually time travel to different worlds where today is a different today.

You have to first start by wearing a trench-coat, all time travelers do these days.

I was able to get this to do exactly what i wanted. Thanks for all the help!

var date Today=Today();

var date EffectiveStart = FirstDayOfMonth([Deprecation Start Date]);
var date EffectiveToday = LastDayOfMonth($Today);

var date ES = $EffectiveStart;
var date ET = $EffectiveToday;

var number MonthsStepOne = (Year($ET) - Year($ES)) * 12;

var number MonthAdjustment = If(Month($ET) >= Month($ES), Month($ET) - Month($ES),  // both ends count as a month, so add 1
     (Month($ET) - Month($ES)));
   
var number Months = $MonthsStepOne + $MonthAdjustment;

Min(Max(0, [Original Amount] - [Original Amount]/[Deprecation Term (months)] * $Months),[Cost])

Great, thx for letting me know.  Please be sure to ask all your questions while I'm trapped in a horrible waiting room waiting for an airplane.  That is why I had the time.

Slightly off topic... Do quickbase automations ignore anything triggered via a webhook or records being modified by another application, much like the way form rules won't trigger off of a webhook (form rules only work when a user opens the record and interacts with it)?

QuickBase Actions and Automation trigger off any change to the database by itself (ie the automation can get itself into a loop), or any other Action, Automation, human input, grid edit, manual import, API - anything database change.  The "trigger" is at the database level and not the interface level.