Suppose that the SONIA yield curve looks like this:

$\backslash$table$[[\frac{\text{M}\text{a}\text{t}\text{u}\text{r}\text{i}\text{t}\text{y}\text{.}}{6\text{m}\text{o}\text{n}\text{t}\text{h}\text{s}},$SONJ$],[5\mathrm{.}20],[\backslash$table$[[12],[$months$]],5\mathrm{.}10],[,],[\backslash$table$[[24],[$month$]],]]$

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 t$$ make a brand new $2-$year bond with semiannual 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?