You need a 30-year, fixed-rate mortgage to buy a new home for $190,000. Your mortgage bank will lend you the money at a 8.1 percent APR for this 360-month loan. However, you can afford monthly payments of only $1,000, 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 $1,000?