Suppose you have just purchased your first home for $$300,000.$ You were able to put $$15,000$ down and finance the difference. You were required to pay for PMI insurance of $30\%$ of the initial loan amount.

Over time you paid down the principal of the loan to $$265,000$ and at that point in time you can no longer make any mortgage payments $($i$.$e$.,$ you default on the loan$).$ If the lender were to foreclose on your property and sell it for $$200,000,$ determine the amount of the loan's principal that the lender was able to recover due to the default.