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

a$)$ Should the borrower refinance if he plans to own the property for the remaining loan term? Assume that the investor borrows only an amount equal to the outstanding balance of the loan.

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

SHOW WORK $($NO EXCEL$)$