In $1897,$ the first Green Jacket Golf Championship was held. The winner's prize money was $$215.$ In $2020,$ the winner's check was

$$2,550,000.$

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

Note: 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 $2053?$

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,1,234,567\mathrm{.}89.$