You need a $15-$year, fixed$-$rate mortgage to buy a new home for $$200,000.$ Your mortgage bank will lend you the money at a $8\mathrm{.}6$ percent APR for this $180-$month loan. However, you can afford monthly payments of only $$950,$ 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 $$950?$

Multiple Choice

$$93,256\mathrm{.}6$

$$376,435\mathrm{.}47$

$$365,142\mathrm{.}41$

$$391,492\mathrm{.}89$

$$104,099\mathrm{.}5$