Offer your thoughts or opinion on the input financial query or topic using your financial background.

Buying a mortgaged house
Based on what you asked and your various comments on other answers, this is the first time that you will be making an offer to buy a house, and it seems that the seller is not using a real-estate agent to sell the house, that is, it is what is called a FSBO (for sale by owner) property (and you can learn a lot of about the seller's perspective by visiting fsbo.com). On the other hand, you are a FTB (first-time buyer) and I strongly recommend that you find out about the purchase process by Googling for "first-time home buyer" and reading some of the articles there. But most important, I urge you DO NOT make a written offer to purchase the property until you understand a lot more than you currently do, and a lot more than all the answers here are telling you about making an offer to buy this property.  Even when you feel absolutely confident that you understand everything, hire a real-estate lawyer or a real-estate agent to write the actual offer itself (the agent might well use a standard purchase offer form that his company uses, or the State mandates, and just fill in the blanks). Yes, you will need to pay a fee to these people but it is very important for your own protection, and so don't just wing it when making an offer to purchase. As to how much you should offer, it depends on how much you can afford to pay. I will ignore the possibility that you are rich enough that you can pay cash for the purchase and assume that you will, like most people, be needing to get a mortgage loan to buy the house. Most banks prefer not to lend more than 80% of the appraised value of the house, with the balance of the purchase price coming from your personal funds. They will in some cases, loan more than 80% but will usually charge higher interest rate on the loan, require you to pay mortgage insurance, etc. Now, the appraised value is not determined until the bank sends its own appraiser to look at the property, and this does not happen until your bid has been accepted by the seller. What if your bid (say $500K) is much larger than the appraised value $400K on which the bank is willing to lend you only $320K ? Well, you can still proceed with the deal if you have $180K available to make the pay the rest. Or, you can let the deal fall apart if you have made a properly written offer that contains the usual contingency clause that you will be applying for a mortgage of $400K at rate not to exceed x% and that if you can't get a mortgage commitment within y days, the deal is off. Absent such a clause, you will lose the earnest money that you put into escrow for failure to follow through with the contract to purchase for $500K.  Making an offer in the same ballpark as the market value lessens the chances of having the deal fall through. Note also that even if the appraised value is $500K, the bank might refuse to lend you $400K if your loan application and credit report suggest that you will have difficulty making the payments on a $400K mortgage.  It is a good idea to get a pre-approval from a lender saying that based on the financial information that you have provided, you will likely be approved for a mortgage of $Z (that is, the bank thinks that you can afford the payments on a mortgage of as much as $Z). That way, you have some feel for how much house you can afford, and that should affect what kinds of property you should be bidding on.