In $1895,$ the first U$.$S$.$ Open Golf Championship was held. The winner's prize money was $$180.$ In $2019,$ the winner's check was $$1,380,000.$

a$.$ What was the percentage increase per year in the winner's check over this period? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ If the winner's prize increases at the same rate, what will it be in $2040?($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

$\backslash$table$[[$a$.$ Increase per year,$f$