I can't see a formal document for lending money to buy a bike, but an IOU would require phrasing like 'for the consideration of which', blah, blah, blah, don't you think?
If the "bike" threw you, how about "house", "yacht", "stately manor", etc? Or are you saying that one would not need to use either "loaned" or "lent" in a formal document?
I suspect without research that some more legal terminology would appear in a formal document regarding the transfer of funds and the responsibility for repayment of same.