Pay an excessive amount for something, as in We paid through the nose for that vacation. The origin of this term has been lost. Possibly it alludes to the Danish nose tax, imposed in Ireland in the 9th century, whereby delinquent taxpayers were punished by having their noses slit. [Second half of 1600s]

To pay unreasonably high prices: “If you visit any major city these days, you had better be prepared to pay through the nose for a hotel room.”