A legal written promise to pay borrowed money back at a fixed rate of interest over a fixed period of time is a

The answer is Promissory Note

Explanation:

The most common document used to register a loan and guarantee this is paid back is a Promissory Note. In this, the parties involved register the amount of money that was borrowed and the borrower promises through the document to pay this amount of money before a fixed specific date. Also, promissory notes register the rate of interest that will be paid by the borrower. Besides this, a promissory note is a legal document that registers the loan and can be used as a legal instrument in case the money is not paid back.