With most homes selling for above appraisal value you will need to pay the difference of purchase price and appraisal price in cash. If you do not have this extra cash it could be very challenging.
Often time buyers will go with a cash offer with a lower purchase price to ensure that the deal does not fall out of escrow last minute because of the buyer's finance contingency or appraisal contingency.
It is also not unheared of to have the seller request that the buyer waives their financing and appraisal contingency for this exact reason.
Good luck on you search!
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