The Chips recently found that they can reduce their mortgage interest rate from $12\%$ to $8\%.$ The value of homes in their neighborhood has been inreasing at the rate of $7\mathrm{.}5\%$ annually. If the Moores were to refinance their house with $$2,000$ in closing costs in addition to the mortgage balance $($$$120,056)$ over a period of time to coincinde with their chosen retirement age in $22$ years, what would the monthly payment be for principal and interest $($closing costs are going to be added to the mortgage$)?$