According to me, it sounds quite formal and if I were you, I
wouldn't hesitate to use it in a formal letter. But, it is Matthew
who is an expert here.
Not an expert, just a native English speaker!
Let me add some "informal" responses:
"So sorry I made problems for you!"
"Oh, I have put you out!"
"Sorry that I caused you problems!"
The original sentence is FINE in a formal letter!!!!!!!!!
There are a few variations of this sentence, but none are
important enough to mention. This sentence works very well.
Matthew