$(25$ pts$)$ Please answer the two questions below. SHOW YOUR WORK FOR ALL PARTS.

$($a$)$ Calculate the implied forward rate for a one$-$year security issued $3$ years from now, assuming semi$-$annual compounding of interest. This would be IFR$6,2$ in the notation used in the slides. Assume the three$-$year spot rate $z_6$ is $2\mathrm{.}983\%$ and the four$-$year spot rate $z_8$ is $2\mathrm{.}883\%.$ These are quoted as annual rates. $($Hint: remember to express the interest rates and periods in $6-$month terms, not annual terms, for your calculations. Also remember that your answer must be expressed in annual terms$)$

$($b$)$ Calculate the implied forward rate for a two$-$year security issued $5$ years from now, assuming semi$-$annual compounding of interest. This would be IFR$10,4$ in the notation used in the slides. Assume the five$-$year spot rate $z_{10}$ is $3\mathrm{.}886\%$ and the seven$-$year spot rate $z_{14}$ is $4\mathrm{.}006\%.$ These are quoted as annual rates. $($Hint: remember to express the interest rates and periods in $6-$month terms, not annual terms, for your calculations. Also remember that your answer must be expressed in annual terms$)$