An investor obtained a fully amortizing mortgage five years ago for $$95,400$ at $11$ percent for $30$ years. Mortgage rates have dropped, so that a fully amortizing $25-$year loan can be obtained at $10$ percent. There is no prepayment penalty on the mortgage balance of the original loan, but $3$ points will be charged on the new loan and other closing costs will be $$2,000.$ All payments are monthly. Assume that the investor borrows only an amount equal to the outstanding balance of the loan.

Required:

a$.$ Should the borrower refinance if he plans to own the property for the remaining loan term?

b$.$ Should the borrower refinance if he planned to own the property for only five more years?