You need a $20-$year, fixed$-$rate mortgage to buy a new home for $$200,000.$ Your mortgage bank will lend you the money at a $6\mathrm{.}1$ percent APR for this $240-$month loan. However, you can afford monthly payments of only $$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

$$231,170\mathrm{.}31$

$$240,417\mathrm{.}12$

$$68,459\mathrm{.}69$

$$54,420\mathrm{.}48$

$$224,235\mathrm{.}2$