Suppose that $3$ years ago you took a mortgage loan for $$216,927$ at $8\mathrm{.}2\%$ for $30$ years, monthly payments. This loan has a prepayment penalty of $5\%$ of the outstanding balance for the first $8$ years of life. The market rate on new mortgages now is $5\mathrm{.}7\%.$ Lenders are charging $6\%$ financing costs on new loans. Your opportunity cost is $5\mathrm{.}7\%.$

If you plan to hold the loan to maturity $($whether refinancing takes place or not$),$ determine whether you should refinance the payoff of the existing loan for the remaining term 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$).$