Given the following information calculate the net benefit of refinancing $($note the benefit may be negative or positive$).$ A home owner has and outstanding mortgage with a remaining term of $20$ years, a remaining balance of $$252,178,$ current payment of $$1,790\mathrm{.}35$ and an interest rate of $6\mathrm{.}74\%.$ The home owner is able to refinance this loan at the same term, but with a new rate of $4\mathrm{.}87\%.$ The expected refinancing charges will be $6\%$ of the loan amount. The home owner is expecting to move when they retire in ten years.