A zero$-$coupon bond with maturity $1$ year and face value $$100$ currently sells for $94\mathrm{.}34$$$.$ A zerocoupon bond with maturity $2$ years and face value $$500$ currently sells for $462\mathrm{.}25$$$.$

$1.$ Estimate the yield to maturity of the $1-$year zero$-$coupon bond.

$2.$ Estimate the yield to maturity of the $2-$year zero$-$coupon bond.

$3.$ Using the yields you estimated in $(1)$ and $(2),$ price a $2-$year coupon bond with F $=1,000$$

and c $=5\%($paid annually$).$

$4.$ Is the yield$-$to$-$maturity of the coupon bond above, below or exactly $5\%?$