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Homebuyers are facing one of the priciest housing markets in history, and that means they need larger mortgages than ever before. While mortgage demand is falling, due to rising interest rates, the size of the average purchase loan application just set a record.

Mortgage applications to buy a home fell 1% last week compared with the previous week, according to the Mortgage Bankers Association’s seasonally adjusted index. Volume was 7% lower than the same week one year ago.