$($a$)$ The $2-$year zero yield is $4\%$ p$.$a$.$ The $24x48$ forward rate is $8\%$ p$.$a$.$ These two rates are semi$-$annual compounding. Relying on the fact that the value of an FRA is zero at inception, compute the $4-$year zero yield.

Please report per annum semi$-$annually compounding rates.

$($b$)$ According to the pure expectation hypothesis, what does the $2448$ forward rate tell us$?$