$*$Half the stated coupon is paid every six months.

Round to the nearest $4$ decimal places for the interest rates in this question $($eg$.0406$ or

$4\mathrm{.}06\%$

$($a$)$ Calculate zero rates for maturities of $6$ months, $12$ months, $18$ months, and $24$ months.

$($b$)$ What are the forward rates for the periods: $6$ months to $12$ months, $12$ months to $18$

months, and $18$ months to $24$ months?

$($c$)$ What are the yields to maturity $($continuously compounded$)$ for each of the bonds?

$($d$)$ Estimate the price and yield $($continuously compounded$)$ of a two$-$year bond providing a

semiannual coupon of $7\%($on a face value of $$100)$ per annum.

$\backslash$table$[[$Bond Principal $($$$),\backslash$table$[[$Time to Maturity$],[($yrs$)]],$Annual Coupon $($$$)*,$Bond Price $($$$)],[100,0\mathrm{.}5,0\mathrm{.}0,97],[100,1\mathrm{.}0,0\mathrm{.}0,96],[100,1\mathrm{.}5,6\mathrm{.}2,102],[100,2\mathrm{.}0,8\mathrm{.}0,103]]$

$*$Half the stated coupon is paid every six months.

Round to the nearest $4$ decimal places for the interest rates in this question $($eg$.0406$ or $4\mathrm{.}06\%$

$($a$)$ Calculate zero rates for maturities of $6$ months, $12$ months, $18$ months, and $24$ months.

$($b$)$ What are the forward rates for the periods: $6$ months to $12$ months, $12$ months to $18$ months, and $18$ months to $24$ months?

$($c$)$ What are the yields to maturity $($continuously compounded$)$ for each of the bonds?

$($d$)$ Estimate the price and yield $($continuously compounded$)$ of a two$-$year bond providing a semiannual coupon of $7\%($on a face value of $$100)$ per annum.