FHA loan APR rate...how do I keep it.?

I was approved for a 100,000 loan for a house at 4.375 APR. The house I'm going to purchase is about 109,000. My loan is through First National bank and they said I'd have to reapply for a loan because the sale price of the home is higher which means my APR will go up based on current rates. I'm happy to pay the extra amount out of pocket to keep my APR. What I don't understand is why-if I'm willing to pay out of pocket for the amount-do they have to renegotiate the loan when I applied for a 120,000 loan to begin with and was only approved for 100,000? If I wasn't approved in the first place why would they approve me now for a higher loan when the interest rates have gone up? Also, if this is true then how to I purchase a house for 100,000 sale price and give legal incentives to take the offer like paying for closing cost ect.? What can I do to keep my APR rate? Any suggestions? Put more money down on the loan?