Calculate Rent per month over time

You could create a measure like

Rent = 
VAR MinDate = MIN( 'Date'[Date] )
VAR MaxDate = MIN( MAX( 'Date'[Date] ), EOMONTH( TODAY(), -1 ) )
VAR SummaryTable = GENERATE(
	SELECTCOLUMNS(
		Rent,
		Rent[Customer],
		Rent[Customer Rent],
		"@StartDate", Rent[Start Date],
		"@EndDate", COALESCE( Rent[End Date], MaxDate )
	),
	FILTER(
		DATESBETWEEN( 'Date'[Date], [@StartDate], [@EndDate] ),
		DAY( 'Date'[Date] ) = DAY( [@StartDate] )
	)
)
RETURN SUMX( 
	FILTER(
		SummaryTable, 
		'Date'[Date] >= MinDate && 'Date'[Date] <= MaxDate
	),
	Rent[Customer Rent] 
)

For each customer it generates a list of dates when the rent would be due, and then sums all those rents which are due during the selected period.