I would argue that this is not unethical and I would say that the young woman’s poor credit (which is not mentioned in the question) helps to make it more ethical. To be clear, I am assuming that the woman lacks the cash to pay (this is clearly stated) and that the financing fee is high because she has bad credit (this is implied, but not stated clearly).
The woman’s credit is important here because it has very much to do with the amount of risk that the firm incurs when it lets her take away the air conditioner. When the firm allows the woman to take the air conditioner and loans her the money, it is taking on risk. Now that she has taken the air conditioner, it can never again be “new” and therefore is no longer as valuable to them as it once was. Because the woman has bad credit, there is a relatively high risk of her defaulting on the loan. In that case, the firm would not have the money it loaned and its air conditioner (if it repossessed it) would be worth less than it once was. Thus, the firm is putting itself at risk by selling to the woman.
Therefore, the financing fee is ethical for two main reasons. First, it helps the woman get an air conditioner that she could not otherwise have had and is therefore beneficial to her. Second, it is higher for her based on the fact that she puts the firm at greater risk of losing money.