You are the vice president of finance for a manufacturer of scuba diving gear. The company is planning a major plant expansion in $5$ years. You have decided to start a sinking fund to accumulate the funds necessary for the project. Your company's investments yield $12\%$ compounded quarterly. It is estimated that $$4,000,000$ in today's dollars will be required; however, the inflation rate on construction costs and plant equipment is expected to average $7\%$ per year for the next $5$ years.

$($a$)$ Use the compound interest concept from Chapter $11$ to determine how much $($in $$)$ will be required for the project, taking inflation into account. $($Use Table $11-1.$ Round your answer to the nearest cent.$)$

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$($b$)$ What sinking fund payments $($in $$)$ will be required at the end of every $3-$month period to accumulate the necessary funds? $($Use Table $12-1.$ Round your answer to the nearest cent.$)$

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