Four Treasury securities data from today's Wall Street Journal are provided below:

Bond TreasurySec. Maturity. AnnualCoupon. Price

A Tbill $6$month $0\%$ $$984\mathrm{.}024$

B Tbill $1$year $0\%$ $$966\mathrm{.}1280$

C Tnote $18$month $3\mathrm{.}875\%$ $$999\mathrm{.}0625$

D Tnote $2$year $4\mathrm{.}625\%$ $$1009\mathrm{.}0625$

The par value is the same for all bonds which is $$1000$

Please note that actual coupons are paid semi$-$annually, i$.$e$.,$ one half of the annual coupon.

$1.$ What is the $1-$year forward rate beginning $6$ months from today?

$2.$ Given the zero prices obtained below. What should be the price of a $2-$year T$-$note with $7\mathrm{.}5\%$ annual coupon $($paid semiannually$)?$ With $1000$ par value per share?

zero price $=$ par value$/(1+$yield rate$)*$ Maturity

a$)$ Yield rate $=$ Excel function rate $=(\mathrm{.}5*2,-1000*0/2,984\mathrm{.}024,-1000)*2=0\mathrm{.}032471$

zero price $=1000/(1+0\mathrm{.}032471)^\mathrm{.}5=984\mathrm{.}15$

b$)$Yield rate $=$ Excel function rate $=(1*2,-1000*0/2,966\mathrm{.}128,-1000)*2=0\mathrm{.}034759$

zero price $=1000/(1+0\mathrm{.}034759)^1=966\mathrm{.}41$

c$)$ Yield rate $=$ Excel function rate $=(\mathrm{.}5*2,-1000*0\mathrm{.}03875/2,999\mathrm{.}0625,-1000)*2=0\mathrm{.}0394$

zero price $=1000/(1+0\mathrm{.}0394)^1\mathrm{.}5=943\mathrm{.}683$

d$)$ Yield rate $=$ Excel function rate $=(2*2,-1000*0\mathrm{.}04625/2,1009\mathrm{.}0625,-1000)*2=0\mathrm{.}041481$

zero price $=1000/(1+0\mathrm{.}041481)^2=921\mathrm{.}928$