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 $1\mathrm{.}976\%$ p$.$a$.$ simple interest rate. The yield rate of first bank bill is $2\mathrm{.}511\%$ p$.$a$.$ simple interest rate and the yield rate of second bank bill is $2\mathrm{.}631\%$ p$.$a$.$ simple interest rate.

a$)$ What is price of first bank bill? Round your answer to three decimal places.

Question $3$Answer

a$.$

$99384\mathrm{.}659$

b$.$

$99380\mathrm{.}849$

c$.$

$99515\mathrm{.}130$

d$.$

$99355\mathrm{.}442$

$($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$.$

$2\mathrm{.}3078\%$

b$.$

$2\mathrm{.}5706\%$

c$.$

$2\mathrm{.}5770\%$

d$.$

$2\mathrm{.}6374\%$