Jay purchased a $150-$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

$2\mathrm{.}87\%$ p$.$a$.($simple interest$)?$ Round your answer to three decimal

places.

a$.495326\mathrm{.}291$

b$.494171\mathrm{.}484$

c$.495249\mathrm{.}136$

d$.495287\mathrm{.}711$

$($b$)$ Assume that John sold this bank bill at a simple interest rate of $2\mathrm{.}87\%$ p$.$a$.$ up to the maturity date of the above bank bill. What is the annualised $($simple interest$)$ yield for this investment from $15$ July $2021$ to $13$ August $2021?$ Round your answer to $3$ decimal places in terms of percentage.

a$.12\mathrm{.}487\%$

b$.11\mathrm{.}266\%$

c$.11\mathrm{.}846\%$

d$.12\mathrm{.}156\%$