Problem $4(25$ marks$)$

We adopt the same setup as in Problem A$3.$ Suppose that another investor would like to invest the capital $($say $$10000)$ for $4$ years and seeking for a return strictly higher than $i_0=3\%.$ You are given that

The investor expects that the future interest rate will go up$.$

The investor demands a minimum return of $i_{\text{m}\text{i}\text{n}}=2\mathrm{.}6\%$

$($a$)$ Calculate the safety margin at current time.

$($b$)$ Suppose that the investor is only allowed to invest the capital into one bond.

$($i$)$ Which bond should he$/$she consider? Explain your answer.

$($ii$)$ The investor invests the capital into the bond suggested in $($b$)($i$)$ and suppose that the interest rate has dropped to $2\mathrm{.}5\%$ after $1$ year. Calculate the safety margin and suggest a strategy for the investor at time $1$ based on what has been discussed in class.