I know per annum is from Latin, but what are the real-world differences between these two phrases? Is one used in certain contexts and the other in other contexts?
From the Oxford Corpus of English:
These example sentences are representative of the most common uses of these two phrases and, as one can see, there is no real difference between per annum and per year in usage.
As kiamlaluno says, per annum is traditionally used more in financial contexts than per year, but these sentences show that per year is also perfectly acceptable.
Annum is the Latin word for year. Its meaning in English has not really diverged at all, so it is basically just a snooty (or jargonistic) way to say year. Fewer people know the word, so it is probably a good word to use if you are trying to bury the truth of something under a blanket of obscure verbiage.
The cynic in me begs to point out that financial institutions and lawyers like to use it...