All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
We have not come across any statements of the scholars regarding the ruling on writing in a case such as the one mentioned in the question; it appears – Allah knows best – that its ruling and method depend on the value of the borrowed object, and the reference in this regard is to the prevailing customs and traditions of the people.
The research published by the magazine of the Islamic Fiqh Committee entitled "Documentation of Debt and Other Financial Transactions" reads, "In regard to other financial transactions, the customs prevalent among the people as their conditions entail have a significant impact in determining whether documentation is obligatory, recommended, or permissible."
Allah knows best.