$16.$ Michael and Sasha own their home, which Michael bought in January $2014$ for $$200,000.$ It is currently assessed for property taxes for $$210,000,$ and aggregate property taxes run $$2,300$ annually. The original mortgage was $$125,000,$ financed for $30$ years at $7\mathrm{.}5\%.$ They have made $108$ monthly payments. Their monthly mortgage payment for principal and interest is $$874.$ Approximately how much of their payments have been applied to their outstanding principal after their $108$th pay

If they would like to refinance their house, what is the outstanding balance on their home mortgage after their $108$th payment?

What is their new monthly payment if they would like to refinance their existing loan for $20$ years at $6\mathrm{.}00\%?$

What is their new monthly payment if they would like to refinance their existing loan for $30$ years at $6\mathrm{.}50\%?$

Which alternative would you recommend and why? $($Consider the following for your answers on cash flow and total cost.$)$