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 $2\%$ p$.$a$.$ simple interest rate. The yield rate of first bank bill is $2\mathrm{.}482\%$ p$.$a$.$ simple interest rate and the yield rate of second bank bill is $2\mathrm{.}692\%$ 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.

Question $4$

a$\mathrm{.}2\mathrm{.}5863\%$

b$\mathrm{.}2\mathrm{.}5929\%$

c$\mathrm{.}2\mathrm{.}6986\%$

d$\mathrm{.}2\mathrm{.}3503\%$