Assume after $10$ years, Federal Reserve implements a new policy to stimulate economic growth by lowering interest rate. As a result, you explore the option of refinancing your mortgage to secure a more favorable rate. PNC Bank offers you $6\%$ interest rate, however the refinancing cost and closing cost $($one$-$time payment$)$ together would be now $7\%$ of the value of your new mortgage. Will you accept the offer and refinance your mortgage? To determine whether you should accept this offer and refinance your mortgage, answer

to the following questions:

$5)$ How much is the remaining principal from your original mortgage at year $10?$

$6)$ How much would be the total amount you need to refinance with your new mortgage $($the remaining principal of your original mortgage plus $7\%$ one$-$time payment$)$

$7)$ What would be your monthly payment for the next $20$ years with $6\%$ interest rate?

$8)$ Compare the answer in part $(7)$ vs$.$ part $(1).$ Will you be willing to refinance your

mortgage