Anthony has just won the Flyball Lottery. He has two options for receiving his prize. The first option is to accept a $$133,000$ cash payment today. The second option is to receive $$20,000$ at the end of each of the next $19$ years and a $$33,500$ lump sum payment in the $20$ th year. Anthony can invest money at a $11\%$ rate.

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$($a$)$ Calculate the present value of the two options. $($For calculation purposes, use $4$ decimal places as displayed in the factor table provided and round final answer to $0$ decimal place, e$.$g$.58,971.)$

Option $1$

Option $2$

Present value

$

$

$($b$)$ If Anthony could invest money at $14\%,$ calculate the present value of the two options. $($For calculation purposes, use $4$ decimal places as displayed in the factor table provided and round final answer to $0$ decimal place, e$.$g$.58,971.)$

Option $1$

Option $2$

Present value

$