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

$\backslash$table$[[,$Maturity,,,,$],[$Rate$,$Month$/$Year$,$Bid,Asked,Change,Ask Yield$],[??,$May $31,103\mathrm{.}5405,103\mathrm{.}5527,\backslash$table$[[+\mathrm{.}3080],[+\mathrm{.}4353]],6\mathrm{.}099],[5\mathrm{.}474,$May $36,104\mathrm{.}5017,104\mathrm{.}6474,+\mathrm{.}4353,??],[6\mathrm{.}188,$May $46,??,??,+\mathrm{.}5470,4\mathrm{.}131]]$

a$.$ In the above table, find the Treasury bond that matures in May $2046.$ 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 $\mathrm{.}0559,$ 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,$$,105\mathrm{.}06ox$