In $1895,$ the first a sporting event was held. The winner's prize money was $$100.$ In $2007,$ the winner's check was $$1,164,000.($Do not round your intermediate calculations.$)$

Required:

$($a$)$What was the percentage increase per year in the winner's check over this period?

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$($b$)$If the winner's prize increases at the same rate, what will it be in $2040?$