Suppose there is a T$-$bond maturing on a coupon

date in exactly six months. Further assume that the

bond is priced at $98\mathrm{.}27\%$ of par and has a

semiannual coupon of $1\mathrm{.}875\%.$

$(1)$ How is the corresponding zero rate computed?

$(2)$ How is the zero rate that corresponds to one

year found? Suppose a T$-$bond that matures in one

year is priced at $99\mathrm{.}302\%$ of par and has a

semiannual coupon of $4\mathrm{.}625\%.$