I'm curious though. Why wouldn't you want your bank to appraise the property before offering the loan? No bank will offer you a loan and without a contingency that it appraises for at least the contract price. Seems to me it is in your best interest to have the home appraised by the bank offering the loan so that you are in a position of knowledge and not just guessing at the value. As the other agents have said, the seller will not have access to the appraisal as you pay the bank for that service and they can only communicate that information to you.
Hope this was helpful and best of luck as it sounds like your deal is a homerun!!!
You've gotten good answers so far - but you also asked, "When i apply for mortgage, dont my bank want to appraise this property before offering me the loan?". That answer is yes, most definitely - but you can get a pre-approval letter and even a conditional commitment from the bank without knowing what property you are buying. Both of these documents will be contingent upon satisfactory appraisal of the property you choose.
Over appraisal is a good thing...it's when the house appraises less than the sale price that there is a problem. A bank will not make a loan for $300,000 when the house appraises at $250,000... but conversely if you offered $250,000 and it appraises at $300,000 unless there's a problem with your credit/qualifying for the loan, you are golden.
Be thankful that you are getting a house that worth more on the current market than you are paying for it.
If this is a short sale and the 3rd party lender's appraisal is more than you offered, your offer will likely be rejected or countered.
If your seller paid for an appraisal and has an agreed contingency in the contract, you may find that the seller may want more$$$
But...it sounds like your bank's requested appraisal came in over your agreed price...be happy and good luck with your new home.