Suppose you have just purchased your first home for $$300,000.$ At the time of purchase, you could only afford to commit to a down$-$payment of $$15,000.$ 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 $$280,000$ and at that point in time you can no longer make any mortgage payments $($i$.$e$.,$ you default on the loan$).$ If the lender were to foreclose on your property and sell it for $$228,000,$ 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.$)$

Group of answer choices

$$57,000$

$$72,000$

$$0$

$$52,000$