Bonus Problem $2($Optional$,30$ marks$)$ The following table shows the market information about some bond portfolios available for purchase in the market: The term structure is assumed to be flat and the annual effective interest rate is currently $\backslash ($ i$\_\{0\}=5\backslash \%\backslash ).$ No short$-$selling is allowed. An investor has $\backslash (\backslash$$ $10000\backslash )$ and would like to invest the money into one of these $3$ bond portfolios for $7$ years. You are given that $-$ The investor expects that the interest rate will raise in future and he would like to seek for an investment who can achieve an IRR strictly higher than $\backslash (5\backslash \%\backslash )$ if his forecast is correct. $-$ The future interest rate level $\backslash ($ i $\backslash )$ is known to be between $\backslash (2\backslash \%\backslash )$ and $\backslash (8\backslash \%\backslash ).($a$)$ Which bond portfolios would be the best for the investor? Explain your answer. $($b$)$ Suppose that the investor also wants to achieve a minimum return of $\backslash ($ i$\_\{\backslash$min $\}=4\mathrm{.}4\backslash \%\backslash )$ even though his guess is wrong. Which bond portfolio will be the best for the investor. Explain your answer.