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$[[$Rate$,\backslash$table$[[$Maturity$],[$Month YYear$]],$Bid,Asked,Change,Ask Yield$],[??,$May $38.,103\mathrm{.}5366,103\mathrm{.}5488,+\mathrm{.}3041,6\mathrm{.}039],[5\mathrm{.}324,$May $43,104\mathrm{.}4978,104\mathrm{.}6435,+\mathrm{.}4317,??],[6\mathrm{.}173,$May $53,??,??,+\mathrm{.}5431,4\mathrm{.}071]]$

a$.$ In the above table, find the Treasury bond that matures in May $2053.$ 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 $\mathrm{.}0538,$ 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,$$,103\mathrm{.}54],[$b$.$ Bid price,$$,103\mathrm{.}48]]$