You are analyzing the following bond on the settlement date of June $08,2021.$ The Bloomberg terminal displays a price of $123\mathrm{.}1685.$

$1.$ Explain the concept behind and calculate the $($i$)$ accrued interest, $($ii$)$ clean price, and $($iii$)$ dirty price and of the bond $(20$ marks$)$

$2.$ Explain the concept of the yield to maturity and use all relevant information to compute its value $(20$ marks$)$

$3.$ Use all relevant information to evaluate the interest rate risk of this bond $(20$ marks$)$

$4.$ Use two different approaches to analyse the impact of a $4-$percentage point increase in interest rates on the bond $(20$ marks$)$