$(8$ points$)$ The current $2-$year zero yield is $6\%$ p$.$a$.,$ semi$-$annual compounding.

The $1224$ forward rate for a $1-$year loan starting from time $1($to time $2)$ is $5\%$

p$.$a$.$ semi$-$annual compounding.

$($a$)$ What is the implied $1-$year zero rate? Please report a per annum semi$-$

annual compounding rate.

$($b$)$ The Fed has just cut their target Fed funds rate. This causes the $1-$year

zero rate to fall by $50$ basis points and the $1224$ forward rate to fall by $10$

basis points. By how much does the $2-$year zero rate fall$/$rise as a result

of the Fed's action?