Principal and Principle
The first, easiest mnemonic device to keep these two words straight is, "The principal is my pal." In other words, the head of a school or a key person at a firm is spelled "-pal." This is also the spelling of "a capital sum placed at interest," the principal of a loan. So as a mnemonic, let's try, "You can't have either a 'loan' or the 'principal' of a loan without an 'a' near the end."
This spelling can also be an adjective, as in "The principal reason for the jury's decision was the testimony of the eyewitness."
"Principle" can only be used as a noun. It refers to a comprehensive and fundamental law, doctrine or assumption, as in a principle of law, a principle of good business, a person of principle. (The adjectival form would refer to a "principled person.")
This is one of dozens of examples of words that came to the English language from the same root but arrived at different times with different spellings and slightly different meanings ("skirt" "shirt"; "chef" "chief"; "hotel" "hostel").
Both these words (and the word "prince") come originally from the Latin word "princeps," meaning "the one who takes the first part" (primus first + capere to take).
Principal came down from Old French and then to Middle English from the Latin word "principalis" meaning "most important."
Principle came down from Middle French and then to Middle English from "principium," meaning "beginning."