You are a lender giving a borrower a $$300$k mortgage. It is a fixed rate fully amortizing $30$ year mortgage. You think the appropriate risk given the discount rate is $4\%.$ Originating the mortgage costs you $($the lender$)$ $$5,000$ in costs $($regulatory and employment related$)$ upfront $($at time $0).$ Given that, what is the lowest interest rate you would be willing to charge? $($Hint: This is a little tricky and we didn't do exactly this in class. Easiest approach is take a guess at the interest rate and solve for the NPV$.$ Don't forget the upfront cost $+$ the fact that you need to give the borrower $$300$k upfront which is like a cost to the lender as well. Then keep guessing interest rates until the NPV is close to $0$ without being negative. Alternatively you could use "goal seek" if you are familiar with that in excel. Both approaches should be pretty fast.$)$

Group of answer choices

$4\mathrm{.}41\%$

$4\mathrm{.}23\%$

$4\mathrm{.}14\%$

$4\mathrm{.}09\%$