Suppose you have just purchased your first home for $500,000. At the time of purchase you could only afford to commit to a down payment of $50,000. 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 $430,000 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 $400,000 (net proceeds), 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 25% of the loan.) ***please show work****