Suppose you have just purchased your first home for $$340,000.$ At the time of purchase you could only afford to commit to a down$-$payment of $$17,000$ and financed the difference.

In order to make the loan, the lender requires you to obtain private mortgage insurance $($PMI$)$ on their behalf. Suppose over time you paid down the principal of the loan to $$300,000$ and at that point in time you can no longer make any mortgage payments $($i$.$e$.,$ you default on the loan$).$ If the lender were to foreclose on your property and sell it for $$200,000,$ what would the lender$$s loss of principal be taking into consideration the protection of mortgage insurance? $($Let$$s assume that the PMI in this case covers the top $30\%$ of the loan.$)$

$-$$$6,700$

$-$$$100,000$

$-$$$3,100$

$-$$$4,300$