Just expanding a little on Jesse´s excellent answer: Rates often (but not always) refer to longer term contracts (reoccurring payments) whereas costs often (but again, not always) refer to a single, fixed cost.

Rates is plural, so if you use the word "rates", then that might give the idea that there is more than one rate that this company charges. A cost is singular, and that would be referring to one specific prices that this company would charge its services at. So, it just depends on what sort of rate/cost this company is charging. Are there multiple prices that these services come at or is there one specific cost that these services are charged at.