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$[[\backslash$table$[[$Maturity$],[$Rate$]],$Month$/$Year$,$Bid,Asked,Change,Ask Yield$],[??,$May $32,103\mathrm{.}5410,103\mathrm{.}5288,+\mathrm{.}3248,5\mathrm{.}919,,,,,,],[6\mathrm{.}052,$May $37,104\mathrm{.}4900,104\mathrm{.}6357,+\mathrm{.}4245,??,,,,,,],[6\mathrm{.}143,$May $47,??,??,+\mathrm{.}5353,3\mathrm{.}951,,,,,,]]$

a$.$ In the above table, find the Treasury bond that matures in May $2047.$ 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 $\mathrm{.}0641,$ what is the bid price in dollars?

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

a$.$ Asked price

b$.$ Bid price