Problem $6-42$ Calculating Loan Payments $[$LO$2]$

You need a $30-$year, fixed$-$rate mortgage to buy a new home for $$335,000.$ Your mortgage bank will lend you the money at an APR of $6\mathrm{.}3$ percent for this $360-$month loan. However, you can afford monthly payments of only $$1,750,$ so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $$1,750?($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

Balloon payment