Converting between currencies with two different date relationships?

So I have a date table, a fact table containing orders with amounts in euros, a booking date and a service date for each order and a foreign exchange rate table with a date column and a column with the conversion rate of the corresponding date.  The FX table has a one to one relationship with the date table and the fact table has a many-to-one relationship with the date table. Can I create a measure that fetches the proper exchange rate for a given order (I'm aware I'll need separate measures for service dates and booking dates) and converts the amounts in the fact table?

Right now I've been merging the FX rate table and the fact table and creating additional columns but that seems untidy.
Help?