The lender(s)/bank(s) will either have a Broker Price Opinion (BPO) or a full Appraisal done to determine fair market value. They will use this figure to decide whether or not to accept your offer. If they do not accept it, they will most likely counteroffer it - unless it is so below market value as to be ridiculous in which case they may just reject your offer or not respond at all and wait for a better offer. Hopefully your Realtor did a Comparative Market Analysis (CMA) on the property (which is similar to a BPO) before submitting your offer.
The Marie Souza Team - Top Selling on Cape Cod
Cape Cod Real Estate Services
You may be assured that the Bank has.
The fact that the seller/homeowner has accepted is meaningless; the Bank is the truw Seller now.
The bank may even ignore you, and look for a better offer. They are not obligated to answer you.
Good luck and may God bless