1. Carissa wanted tickets to the concert so badly that she was willing to pay double for them. She paid through the nose , but she made it to the concert.
2. Peter‘s parents said he couldn’t go out until he finished his chores, so Peter promised to do his sister’s chores for a whole week if she would do his for a day. He had to pay through the nose, but it was worth it to him.

Compare to: cost (someone) a mint; cost (someone) an arm and a leg. The expression usually refers to paying money (opt.1), but it can also refer to exacting other kinds of payment such as trading work, making someone feel very guilty, etc.