We have accepted an offer on our house for 160,000.00. What if it appraises for more than the offer?

You had better hope it appraises for more than the offer! If it didn't, then your deal would fall through. No lender will lend more money for a house than it's worth. I'm sure there's a clause in your purchase agreement that mentions a contingency on the property appraising for at least the amount of the offer. The buyer's agent wouldn't be doing his job of protecting the buyer, if he didn't include such verbiage.