A stock is currently priced at $50$ and pays $0\mathrm{.}5$ dollar quarterly dividends, with the first coming $1$ month from today. The current time point is t $=0$ and the continuously compounded risk$-$free interest rate is $6\%.$ For simplicity, take $1$ month as $1/12$ years.

Based on the above information, answer questions $1$ and $2.$

$1.$ Find the price of the forward that delivers $1$ share of the stock at time T $=0\mathrm{.}8.$

A$.50\mathrm{.}15$

B$.50\mathrm{.}92$

C$.51\mathrm{.}69$

D$.52\mathrm{.}46$

E$.$ None of the above is close

$2.$ Assuming So$3=48.$ Find the time t $=0\mathrm{.}3$ price of a prepaid forward that delivers $1$ share of the stock at time T $=0\mathrm{.}8.$

A$.47\mathrm{.}01$

B$.47\mathrm{.}48$

C$.47\mathrm{.}96$

D$.48\mathrm{.}44$

E$.$ None of the above is close