The Monroes have $$139,937$ remaining on their home mortgage $(5\mathrm{.}25\%$ for $30$ years$)$ their most recent annual payment was $$10,267.$ Current mortgage rates are $3\mathrm{.}5\%$ for $15$ years and $4\%$ for $30$ years. Closing costs would be $3\%$ of the amount financed and would be paid at closing. If they refinance, how much will they save over the life of the mortgage for a $15-$year or $30-$year mortgage? Which mortgage should they select?