Each bank has its own set of financial circumstances.  The carrying cost may vary, but not having the asset on the books is of primary importance to the bank.  Reasonable offers that do not result in the bank investing further dollars into the property is also very important.  The lost interest on the mortgage, although a foreclosure judgment will allow for accrual of interest on the amount owed, is realy only a minor consideration.  Attorney costs have been built into the judgment,  Realtor commissions have not. 

Usually, but not always, the appraised value of the foreclosed property is less than what is owed.  If a bank can take an offer from a good buyer for, say $80,000, it may decide to sell and recoup that part of its investment now and to pursue the shortfall through other means.  Where the property is located, how large a pool of potential buyers, condition of the property and other factors will all play into a decision to sell at a particular price.

The bottom line is that there is NO MAGIC FORMULA that someone can determine what carrying costs a lender may incur such as property taxes, etc.  The best thing to do?  Look in the Registry of Deeds and find out what the amount of the judgment is and what the original loan balance was from the mortgage deed or deed of trust.