To calculate the number of years until maturity, assume that it is currently May $2022.$ All of the bonds have a $$1,000$ par value and pay semiannual coupons.

$\backslash$table$[[$Maturity$,,,,],[$Rate$,$Month$/$Year$,$Bid,Asked,Change,Ask Yield,,,,,$],[??,$May $29,102\mathrm{.}725,102\mathrm{.}915,+\mathrm{.}3204,2\mathrm{.}18,,,,,],[3\mathrm{.}850,$May $32,103\mathrm{.}168,103\mathrm{.}823,+\mathrm{.}4513,??,,,,,],[4\mathrm{.}125,$May $38,??,??,+\mathrm{.}6821,3\mathrm{.}87,,,,,]]$

a$.$ In the above table, find the Treasury bond that matures in May $2038.$ What is the asked price of this bond in dollars?

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

b$.$ If the bid$-$ask spread for this bond is $\mathrm{.}0628,$ what is the bid price in dollars?

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

$\backslash$table$[[$a$.$ Asked price,$$,103\mathrm{.}82],[$b$.$ Bid price,$$,100\mathrm{.}10]]$