You need a 25-year, fixed-rate mortgage to buy a new home for $250,000. Your mortgage bank will lend you the money at a 7.1 percent APR for this 300-month loan. However, you can afford monthly payments of only $900, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment.

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How large will this balloon payment have to be for you to keep your monthly payments at $900?