$1.$ Your coin collection contains $441948$ silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in $2032,$ assuming they appreciate at an annual rate of $9$ percent?

A$.$ $$62,499\mathrm{.}81$

B$.$ $$61,274\mathrm{.}32$

C$.$ $$10,636\mathrm{.}85$

D$.$ $$59,436\mathrm{.}09$

E$.$ $$58,210\mathrm{.}60$

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$2.$ In $1904,$ the first Putting Green Championship was held. The winner's prize money was $$180.$ In $2016,$ the winner's check was $51,178,000.($Do not round Intermediate calculations.$)$

a$.$ What was the percentage increase per year in the winner's check over this period?

Interest Rate $=\_\_\_\_\_\%$

b$.$ If the winner's prize increases at the same rate, what will it be in $2049?$

Future Rate $=\_\_\_\_\_-$