Consider a balloon mortgage loan with a face amount of $$400,000.$ At an annual interest rate of $5\%,$ the monthly payment is $$2,147\mathrm{.}29$ Although payments are based on a $30-$year amortization schedule, the loan has a $10-$year term to maturity. Determine the required balloon payment at the end of the term to maturity.

$($Input your answer as a positive number, rounded to the nearest whole dollar and without the $ sign, e$.$g$.,100,000)$