I assume you get this info from websites like Zillow.
If you have an agent just tell them to send the offer
that you want. I assume you're doing a conventional loan
since the data suggest it won't go standard FHA.
Hope this helps.
Based on what information you have provided here, I cannot answer your question. How do you know how much a bank paid for a property? I assume they did not "pay" for the property, but rather loaned money to a buyer who later defaulted, that is why it is now an REO (bank owned). How much the bank loaned on this property at some unknown time in the past, tells me nothing about what is a fair offer to make on that home now.
The only thing you should base your offer price on is the current comps, the market, and the condition of the home. If the bank has already priced the home below comps, then they have already factored in these variables, and you would have trouble lowballing them. If the bank priced the home higher, then you may get them to consider your offer.
One other item that is important in todays REO market is that the banks do care about your qualifications. They want to see higher down payments, higher good faith deposits, good credit, good fico scores, proof of funds, etc. The more qualified buyer would have a better chance of getting a low offer accepted.
If you want the information that you need to make a reasonable offer, then contact me at: