In $1895,$ the first U$.$S$.$ Open Golf Championship was held. The winner$$s prize money was $$180.$ In $2019,$ the winner$$s check was $$1,500,000.$

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 $2048?($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$