You are given the following spot interest rates:

The rates are convertible semi$-$annually. For example,

$a(0\mathrm{.}5)=1+\frac{0\mathrm{.}0412}{2},a(1)=(1+\frac{0\mathrm{.}0438}{2}{)}^2.$

Calculate the $k-$year deferred $1-$year forward rates for $k=1,2,3$ and also the $1\mathrm{.}5-$year

and $2\mathrm{.}5-$year par yields. All rates are convertible on a semi$-$annual basis, and the par

yields are calculated assuming bonds pay semi$-$annual coupon.