I am selling my house prior to the end of it's term and I am not buy another house. Besides a penalty for not refinancing with my bank what are the other costs that I will incurr? Is there a way that I can avoid the prepayment penalty by investing my equity?

Unless your agreement indicates you have a prepayment penalty, you don't have one. The vast majority of mortgages do not have them. If you do, then I believe you are bound to it, but you should seek the services of an attorney to make sure.