$1.(20$ points$)$ Assume the following government bonds are traded, and they pay annual

coupons:

Bond A Bond B

Face value $$1,000$ $$1,000$

Annual coupon rate $5\%10\%$

Maturity $($years$)22$

Price $$990\mathrm{.}00$ $$1,100\mathrm{.}00$

$($a$)$ What are the $1-$year spot rate, the $2-$year spot rate, and the forward rate between

years $1$ and $2?$

$($b$)$ What is the price of Bond C with a $2-$year maturity, $8\%$ coupon rate, and $$1,000$

face value? What is its yield to maturity?