In $1895,$ the first a sporting event was held. The winner's prize money was $$200.$ In $2007,$ the winner's check was $$1,172,000.($Do not round your intermediate calculations.$)$

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 $2040?$