When the Hamilton$$s purchased their home they took out a $$300,000$ mortgage with a $30-$year term and an interest rate of $8\%.$ The lender requires PMI because the borrower's down payment is less than $20\%$ of the home's value. The PMI rate is $0\mathrm{.}4\%$ of the loan amount annually, and the borrower pays it monthly.

The PMI covered the lender up to $28\%$ of the original loan amount.

Unfortunately, after being in the home for seven years, the Hamilton$$s defaulted on the mortgage and the lender foreclosed.$$ At foreclosure, the lender auctioned the home and received $ $225,000$ for the home.$$ What was the lender$$s loss in this loan?

$$26,489$

$$62,432$

$$84,000$

$$0$