Risk$-$free zero$-$coupon government bonds have the following terms and market prices.

$\begin{array}{cc}\text{Z}\text{e}\text{r}\text{o}\text{c}\text{o}\text{u}\text{p}\text{o}\text{n}\text{b}\text{o}\text{n}\text{d}\text{s}& \text{P}\text{r}\text{i}\text{c}\text{e}\text{s}\\ 1-\text{y}\text{e}\text{a}\text{r}& \text{\$}985\mathrm{.}74\\ 2-\text{y}\text{e}\text{a}\text{r}& \text{\$}967\mathrm{.}28\\ 3-\text{y}\text{e}\text{a}\text{r}& \text{\$}941\mathrm{.}78\\ 4-\text{y}\text{e}\text{a}\text{r}& \text{\$}912\mathrm{.}44\end{array}$

A$.$ Calculate the price of a $4-$year coupon bond that pays $8\%$ annual coupon payment. Assume the face value of this coupon bond is $$1,000.(6$ points$)$

B$.$ Calculate the implied forward rates for year $2$ and year $4.(4$ points$)$