You are a lender giving a borrower a $$250k$ mortgage. It is a fixed rate $6\%$ fully amortizing $30$ year mortgage. You think the appropriate risk given the discount rate is $5\%.$ However, you know the Federal Reserve will cut rates at the end of month $44$ of this mortgage and the borrowers are very savvy so you know they will pay off the whole balance at that point $($and get a new refinanced mortgage with somebody else$).$ What is the NPV of making this loan? $($Hint: This is a $30-$year mortgage so monthly payment math is the same, but you will only get $44$ of those $+$at the end of month $44$ you also get whatever balance is left.$)$ Round to the closest $$1k.$

$$8$k

$$25$k

$$5k$

$$15$k