I would not worry about the buyer not signing the extension of time addendum before you do. Since your agent is preparing it, you are basically offering to extend the contract, so you sign first, and the buyer has an option to sign or walk. If the loan contingency lasts till the loan is funded, which any competent buyer's agent should check on the initial offer, then the buyer gets back their earnest money deposit if the transaction does not close due to lack of loan obtained by any stated time.
When you make an offer to extend time, you can ask, if you have not already, to see the buyer's proof of funds to close. Make showing this proof as a condition of the extension. This will answer your question as to whether they have the money to pay the down payment and their share of closing costs. You should hope that they have considerably more money than necessary in case the appraisal comes in too loan and the bank won't loan the amount of money the buyer anticipated needing. You can also ask, at this point to look at their income, such as most recent pay stubs, and do a rough calculation of whether they have the income to qualify for their loan.
I would also ask if they took the loan to a broker rather than to a correspondent bank or retail bank. Going to a broker often slows things down a lot. It may also be a sign that they knew they would have trouble getting the loan. Ask, if they are with a broker, to which bank the loan has been committed. I f the answer is none yet, then you have a worry. At that point, I would look at back up offers. I would suggest your agent call back the next highest bidders and see if they might still be interested in your home.
One technique you might want to employ now is to make an offer to extend time ON THE CONDITION, that the loan contingency expire automatically, meaning without having to be released, by a certain time. This will put the buyer in the position of evaluating whether they can risk the loan not coming in. If they can't, and are not sure the loan will come in, they'll back out. If I were advising my client on this, I would give the buyer at least ten days before that expiration of loan contingency. The appraisal won't get to the loan officer for about five days after the appraiser visits the home. If the appraisal comes in too low to support the loan (common now in a market of rising prices for regular sales but appraisal values being held back by short sales and REO pricing and delays in closing at those prices), then the buyer either has to have more money for down payment or give up the transaction. Please give them time to find that out before they have to fish or cut bait.
If you decide not to extend the contract, then ask your agent to send a notice to perform. The agent can explain the timelines that then come into play before you place the home back on the market. Placing it back on the market, if you don't already have a back-up offer and your home is in the lower end of the price range, may be a blessing; prices are moving up rapidly in the lower end of the price range.
I hope this helps ease your anxiety and gives you some direction you can discuss with your agent.
First, i'm sorry that you find yourself in this predicament, and as much as I--or any other agent here on Trulia would like to help you--the intiricacies of your contract and the papers signed will be known only to your agent and to the buyer's agent. So talk with your agent, and I'm sure he/she will help you understand your current situation and your options.
Generally, however, as the others have already noted, unless the extension of time is signed by all parties (buyer and seller), then the extension was not granted. You should be able to get and to see an executed copy of this extension--just call your agent to see it.
if the extension has not been signed, you do have several options including noticing the buyers to request performance, finding out what and why the contract has not been executed, and terminating the contract for cause to find a new buyer. Each of these options and any other actions can be better explained by your agent.
I do find it troubling, however, that the appraiser has just shown up and that the inspection is just getting started especially since these coningencies are normally removed in the first 17 days after the contract is signed. If the contract is now expiring, I guess a good question to ask is why the contingencies were not removed sooner, and if the buyers actually have the capacity to close escrow even with an extension. Again, talk with your agent to get more information. I'm sure there's a lot more to this than meets the small paragraph of facts you're allowed when asking a question.
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Also a contract does not just terminate on the final day like you think it does. In the offer contract there is a clause that states that 3 days after a deadline the seller can give the buyer a notice to perform. In the notice to perform the seller will have their requests such as extended time periods.
Also, check out my Santa Clara County Real Estate blog at http://BayAreaConnect.com for real estate news, weekly new listing photos, and market reports.
If you have any further questions give me a call, (408) 840-3852, or shoot me an email at Thomas.Feng@gmail.com