In year $2020,$ you won the championship in a Singapore TV show. You can choose any one $(1)$ of the following reward packages.

Option $1$: You will receive an amount of $10,000$ in $10$ years.

Option $2$: Starting from today, you will get annual payments of $900$ for $10$ years.

Option $3$: Beginning $1$ year from today, you will get annual payments for $8$ years. The first payment is $1000$ and the amount would increase $3\%$ yearly.

$($a$)$ Compute the present value of each option if the discount rate you used is $5\%.$

$($b$)$ Assume that the discount rate is not given. Show your opinion on how to select the option to maximize your reward in the year of $2020.$