An investor obtained a fully amortized mortgage five years ago for $$95,000$ at $11\%$ annual rate for $30$ years. The mortgage rate dropped, so that a fully amortized $25-$year loan can be obtained at $10\%.$ There is no prepayment penalty on the mortgage balance of the original loan, but $3$ points will be changed on the new loan and other closing costs will be $$2,000.$

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

b$.$ Would your answer to part $($a$)$ change if he planned to own the property for only four more years?