In $1896,$ the first Green Jacket Golf Championship was held. The winner's prize money

was $$200.$ In $2018,$ the winner's check was $$2,460,000.$

a$.$ What was the annual percentage increase 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 $2050?($Do not round

intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,$

$1,234,567\mathrm{.}89.)$