Use this information to answer the next $4$ questions.

You purchased a house for $$535,000$ exactly $9$ years ago using a $75\%$ LTV fixed$-$rate mortgage amortized over $30$ years at $6\mathrm{.}25\%($monthly$).$ This loan had a $5\%$ prepayment penalty associated with it$.$ You are thinking about refinancing your outstanding balance and have decided to pay any costs incurred if the process out of pocket. The best rate currently available is $2\mathrm{.}25\%$ for $30$ years with monthly payments. This new loan has a $1\%$ origination fee. $3$ discount points, and no prepayment penalty. You intend to remain in the home for $11$ more years.

$1.$ Compute the total costs to refinance.

$2.$ Compute the total payoff on the old mortgage at the end of year $20.$

$3.$ Compute the payment on the new mortgage.

$4.$ Compute the return to refinancing.