Suppose that $3$ years ago you took a mortgage loan for $$291,269$ at $8\mathrm{.}4\%$ for $30$ years, monthly payments. This loan has a prepayment penalty of $5\%$ of the outstanding balance for the first $7$ years of life. The market rate on new mortgages now is $4\mathrm{.}8\%.$ Lenders are charging $6\%$ financing costs on new loans. Your opportunity cost is $4\mathrm{.}8\%.$

Suppose you want to take $$24,576$ of equity out of the house and you want no out$-$of$-$pocket expenses, and you refinance for a $20-$year term. Also assume that the contract rate on the new loan remains at $4\mathrm{.}8\%$ and the loan is held to maturity. Determine whether you should refinance the payoff of the existing loan by calculating the NPV$.$

Note: If your NPV is negative, make sure to enter it as a negative number $($should not refinance$).$ If your NPV is positive, make sure to enter it as a positive number $($should refinance$).$