Calcuate the closest less than date

// DAX
// Calculated Column in 'Charge Activity' table
RateOnDate =
CALCULATE(
    VALUES( 'Rate Information'[Rate] )
    ,TOPN(
        1
        ,CALCULATETABLE(
            'Rate Information'
            ,'Rate Information'[Employee ID] = EARLIER( 'Charge Activity'[Employee ID] )
            ,'Rate Information'[Rate Effective Date] <= EARLIER( 'Charge Activity'[Charge Date] )
        )
        ,'RateTable'[RateEffectiveDate]
        ,DESC
    )
)

CALCULATE() allows us to set a filter context in which to evaluate an expression. Argument 1 is the expression to evaluate. Arguments 2..N define filter contexts that are combined in a logical and to evaluate Argument 1 in.

Argument 1 is VALUES( 'Rate Information'[Rate] ). VALUES() returns the distinct values in a field based on filter context. If the number is distinct values is <= 1, then the result of VALUES() can be coerced to a scalar.

TOPN() returns the top N rows of some table based on sort criteria we define. We want to return one row of the table defined in CALCULATETABLE() sorted by [RateEffectiveDate] in descending order.

CALCULATETABLE() does for table expressions what CALCULATE() does for scalar expressions. We want to return a subset of 'Rate Information'. The first filter we apply to 'Rate Information' is to return only values where [Employee ID] matches the [Employee ID] in 'Charge Activity', where we are defining this calculated column. EARLIER() allows us to reach back to the row context in 'Charge Activity' from inside the CALCULATETABLE().

The second filter argument (third overall argument) to CALCULATETABLE() does a similar pattern, but based on the value of [Charge Date] in the row context of 'Charge Activity'.

Using the result of this TOPN() as a filter, CALCULATE() will return only the [Rate] that matches the criteria you defined in your post.

A relationship is unnecessary between these tables for this calculated column to work.