You need a $20-$year, fixed$-$rate mortgage to buy a new home for $$180,000.$ Your mortgage bank will lend you the money at a $8\mathrm{.}1$ percent APR for this $240-$month loan. However, you can afford monthly payments of only $$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

$$51,027\mathrm{.}65$

$$67,263\mathrm{.}68$

$$338,044\mathrm{.}47$

$$327,903\mathrm{.}13$

$$351,566\mathrm{.}25$