Jane wanted to purchase a computer for home use and for her young children to use for school work and entertainment. On January 15, Jane went to Dealer, a retail store specializing in computers, and told a salesperson of her family's needs. She was shown a computer that she was told would suffice. She agreed to buy the computer and told Dealer that she would have to borrow the money to pay for it. Dealer agreed to finance the sale and gave Jane $3,000 in credit to buy the computer. Jane took delivery and signed a security agreement that described the computer and granted Dealer a security interest in it. Dealer did not file a financing statement.

Immediately after purchasing the computer from Dealer, Jane changed her mind about how she would use it. Jane had just begun work as an independent consultant, so she took the computer to her office and began using it for business purposes. She did not inform Dealer of this change of use.

On May 1, Jane borrowed $25,000 from Bank as operating capital for her business. She executed a security agreement granting Bank a security interest in her office machinery, including the computer. Also on May 1, Bank filed a valid financing statement in all proper public offices.

Jane defaulted on the loans to both Dealer and Bank. On December 1, Dealer peacefully repossessed the computer. Both Dealer and Bank claim a security interest in the computer.

As between Dealer and Bank, whose security interest takes priority?