You need a $30-$year, fixed$-$rate mortgage to buy a new home for $$290,000.$ Your mortgage

bank will lend you the money at a $5\mathrm{.}85$ percent APR $($semi$-$annual$)$ for this $360-$month loan.

However, you can afford monthly payments of only $$1,300,$ 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 $$1,300?$

$(2$ point$)$