Angela made an $180-$day investment arrangement involving two consecutive $90$ day $$100,000$ bank bills. The maturity proceeds of the first bill will be used to purchase the second bank bill. The remain surplus cash after $90$ days will be invested at $2\mathrm{.}18\%$ p$.$a$.$ simple interest rate. The yield rate of first bank bill is $2\mathrm{.}235\%$ p$.$a$.$ simple interest rate and the yield rate of second bank bill is $2\mathrm{.}664\%$ p$.$a$.$ simple interest rate.

$($b$)$ What will be the annualised $($simple interest$)$ yield rate on Angela's $180-$day investment? Express the result as a percentage and round it to four decimal places.

a$.2\mathrm{.}4276\%$

b$.2\mathrm{.}4553\%$

c$.2\mathrm{.}6712\%$

d$.2\mathrm{.}4481\%$