These two have no overlap in meaning whatsoever, which is unusual — most confusable pairs are at least cousins. "Principal" and "principle" are unrelated in sense and merely happen to sound the same. That makes the error especially visible when it lands in something formal, and it lands in formal writing more than most, because both words belong to contracts, finance and academia.
As a noun: the head of a school, the main party in a transaction, or the original sum of a loan. As an adjective: main or most important.
A noun only. A fundamental truth, rule, or standard of behaviour.
Principal and principle sound identical, and both come from the same Latin root meaning first. They split into different jobs.
Principal means main or most important (the principal reason), and as a noun it names the person or thing that is first: a school principal, the principal on a loan (the amount borrowed, before interest), or the principal in a business deal. Principle is only ever a noun, meaning a basic rule, truth or belief: the principles of physics, a person of principle.
Two memory tricks cover almost every case. The principal of a school is your pal. And principle ends in -le, like rule, which is what a principle is.
She refused on principal.
✓She refused on principle.
She refused because of a belief, a rule she holds: principle.
The school principle announced the new term dates.
✓The school principal announced the new term dates.
The head of a school is the principal. Your pal.
Our principle concern is safety.
✓Our principal concern is safety.
This means main concern, so the adjective principal.
Quick way to remember
Remember that a principal is your pal — a person. And a principle is a rule, both ending in "-le." If the word is describing a person, an amount of money, or means "main," it takes the "a."
Is it "principal investigator" or "principle investigator"?
Principal investigator: the lead researcher on a study, the main one.
On a loan statement, which is it?
Principal. It is the original amount borrowed, as opposed to the interest charged on it.