Work through the following mortgage scenario with Four $(4)$ parts:$1.$ Borrower has a $30-$year mortgage at $6\%$ based on $$500,000.$What is the monthly payment $($principal and interest payment$)$ of this mortgage? $(4$ points$)2.$ After $8$ years, what is the remaining balance? $(3$ points$)3.$ At the end of the eighth year $($based on remaining balance found in Number $2$ above$),$ the borrower has the ability to refinance that remaining balance with a $20-$year mortgage with an interest rate of $4\%$ If the balance in Number $2$ above is refinanced with a $20-$year mortgage with an interest rate of $4\%,$ what would the new monthly payment$($ principal and interest payment$)$ be for the new loan? $(3$ points$)4.$ Assuming that there is a prepayment penalty of $$6,000$ to pay off the original mortgage used in Number $1($based on $30$ years, $6\%,$ $$500,000)$ and $$4,000$ in costs to obtain the new loan, how many months would you need to hold the property with the new mortgage as described in Number $3$ to offset the costs of the refinance?