In $1899,$ the first Green Jacket Golf Championship was held. The winner$$s prize money was $$235.$ In $2018,$ the winner$$s check was $$2,670,000.$

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 $2055?($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,1,234,567\mathrm{.}89.)$