You would like to buy a house that costs $$350,000.$ You have $$50,000$ in cash that you can put down on the house, but you need to borrow the rest of the purchase price. The bank is offering you a $30-$year mortgage that requires annual payments and has an interest rate of $9\%$ per year. You can afford to pay only $$27,740$ per year. The bank agrees to allow you to pay this amount each year, yet still borrow $$300,000.$ At the end of the mortgage $($in $30$ years$),$ you must make a balloon payment; that is$,$ you must repay the remaining balance on the mortgage. How much will be this balloon payment?

Hint: The balloon payment will be in addition to the $30$th payment.

The balloon payment is $$,($Round to the nearest dollar.$)$