The lender can discount the opening bid, or add the accrued interest on the loan to the published bid. It is impossible to know for sure which lenders will discount the opening bid. Often the lender is the servicer of the loan for another investor, and the opening bid is set by the actual investor. There could also be additional interests involved, such as the existence of a mortgage insurance policy, which may cause the lender to set the opening bid at the full amount owed on the loan.
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