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Patricia wants to buy a car when she graduates from Central University $4$ years from now. She believes that she will need $$29,000$ to buy the car.

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$($a$)$ Calculate how much money Patricia must put into her savings account today to have $$29,000$ in $4$ years, assuming she can earn $8\%$ compounded annually. $($For calculation purposes, use $4$ decimal places as displayed in the factor table provided and round final answer to $0$ decimal place, e$.$g$.58,975.)$

Amount

$

$($b$)$ Calculate how much money Patricia must put into her savings account today to have $$29,000$ in $4$ years, assuming she can earn $8\%$ compounded semiannually. $($For calculation purposes, use $4$ decimal places as displayed in the factor table provided and round final answer to $0$ decimal place, e$.$g$.58,975.)$

Amount

$