Jay purchased a $90-$day $$500,000$ bank bill $($at a simple interest rate$)$ on $15$ July $2021.$ The purchase price was $$490,550.$ He sold this bank bill on $13$ August $2021.$

$($a$)$ What was his selling price, if he sold this bank bill at a yield of $3\mathrm{.}52\%$ p$.$a$.($simple interest$)?$ Round your answer to three decimal places.

a$.497075\mathrm{.}832$

b$.497028\mathrm{.}180$

c$.495697\mathrm{.}616$

d$.497123\mathrm{.}494$