A player lands on your property and owes you $16. They hand you a $100 bill and ask you to pay them back $84.
Are you obligated to exchange their money to the banker for smaller denominations in order to pay them back?
A player lands on your property and owes you $16. They hand you a $100 bill and ask you to pay them back $84.
Are you obligated to exchange their money to the banker for smaller denominations in order to pay them back?
Yes, you must give them the correct change.
This is not an issue of a specific rule, but rather just one of how "paying things" in general works, both in games and real life. If you owe someone $16, a valid way to pay that $16 is to give them $100 and ask for $84 back. If the person doesn't have $84 to give you in change; then the two of you work out how to get that change from the bank... there's no difference between you making change and giving the other person exactly $16, or the other person making change with your $100 and returning $84 to you.
In case a rules quote does help:
PAYING RENT… When you land on property owned by another player, the owner collects rent from you in accordance with the list printed on its Title Deed card.
The key being that they can only collect the amount printed on the Title Deed card. They aren't allowed to collect any extra.
If you mean "can you hand the $100 back and tell them to give you exact change", then yeah, I guess you can, but it's kinda a jerk move (although you say in a comment that your brother is giving you large bills deliberately to annoy you, in which case there would be some justification). If you mean "can you just keep the $100 and not give any change back", a common sense reading says that would not be allowed. Not only would that violate the intent of giving the large bill, but there's no mechanism for people to just hand any amount they want to another player. The rules say
When you land on property owned by another player, the owner collects rent from you in accordance with the list printed on its Title Deed card.
https://www.hasbro.com/common/instruct/monins.pdf
So paying more than the rent owed is not supported by the rules.