As a rule of thumb, formal = no contractions. Who are you writing this letter to? We use contractions in conversation, but when we write it's usually better to spell it out. Does this help?

When you are writing to somebody not mother tongue English, try to avoid all contractions with the exception of the very basic ones (don't, doesn't, didn't; keep /I am/ in its full form) You will widen the audience of people that fully understand you.

Typically, using contractions is not proper, but if you were writing to your friend, relative, etc. contractions are fine. When in doubt, just avoid using contractions.