Apollo Enterprises has been awarded an insurance settlement of $$6,000$ at the end of each $6$ month period for the next $12$ years. $($Round your answers to the nearest cent.$)$

$($a$)$ As the accountant, calculate how much $($in $$)$ the insurance company must set aside now at $6\%$ interest compounded semiannually to pay this obligation to Apollo.

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$($b$)$ How much $($in $$)$ would the insurance company have to invest now if the Apollo settlement was changed to $$3,000$ at the end of each $3$ month period for $12$ years and the insurance company earned $8\%$ interest compounded quarterly?

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$($c$)$ How much $($in $$)$ would the insurance company have to invest now if the Apollo settlement was paid at the beginning of each $3$ month period rather than at the end?

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