Reuvain borrowed money from Shimon, and both are unsure if it was ever payed back. Now, of course Shimon can't claim any money from Reuvain, but if Reuvain wants to pay him back out of doubt, should he be worried about paying interest?
In The Laws of Ribbis (chapter 4, section D, paragraph 25, page 88), Rabbi Yisroel Reisman writes:
It is important that both the borrower and lender keep accurate records of how much is owed. When records are not kept, there may be uncertainty regarding the balance which is owed. In this case, the borrower may pay the lender an amount of money which is great enough to assure that the loan is paid up. Although it is possible that he is actually returning more than he borrowed, this is not considered Ribbis. Preferably, the borrower should stipulate that if he is overpaying, the extra moneys are an outright gift and are not intended as a Ribbis payment.