Suppose that the SONIA yield curve looks like this:

Maturity SONIA

$6$ months $5\mathrm{.}20\%$

$12$ months $5\mathrm{.}10\%$

$18$ months $4\mathrm{.}90\%$

$24$ months $4\mathrm{.}80\%$

a$)$ What would be the price of a two$-$year, $1,000$ par bond that pays $4\mathrm{.}5\%$ fixed coupon interest semi$-$annually? $($Assume a coupon payment has just been paid$).$

b$)$ What fixed coupon rate would be required to make a brand new $2-$year bond with semi$-$ annual coupons price at par?

c$)$ What is the $180-$day forward rate for borrowing$/$lending between days $180$ and $360$ implied by the yield curve above?

d$)$ What is the $180-$day forward rate for borrowing$/$lending between days $540$ and $720$ implied by the yield curve above?