Not too sure what you want (are you wanting the exchange rate for each month, for the latest date in the month). If so, you could try,
select MyDate, ExchangeRate from MyTable
where MyDate in (select max(MyDate) from MyTable group by Year(MyDate), Month(MyDate))
Personally, I hate these subselects, and would rather create a view based on the subquery, and join the view and table back together, but as there's only one field to join on, I guess it's OK. The subselect is producing a list of dates, which are the latest dates for each month in the table (If you always have less than one years data, you can dispense with the Year(MyDate) bit). Hope this helps