You've just joined the investment banking firm of Dewey, Cheatum, and Howe. They've offered you two different salary arrangement You can have $$7,100$ per month for the next three years, or you can have $$5,800$ per month for the next three years, along with a $$31,500$ signing bonus today. Assume the interest rate is $5$ percent compounded monthly.

a$.$ If you take the first option, $$7,100$ per month for three years, what is the present value?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$.$ What is the present value of the second option?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

Answer is complete but not entirely correct.

$\backslash$table$[[$a$.$ Value of first option,$$,177,221\mathrm{.}92x$