The yields on $1-$year, $2-$year and $3-$year, risk$-$free, zero$-$coupon bonds are $y_1=2\%,$

$y_2=2\mathrm{.}5\%$ and $y_3=3\%,$ respectively.

a$.$ What is the value of a $3-$year, risk$-$free bond with a coupon rate of $4\%($annual

coupons$)$ and a face amount of $$1,000?$

b$.$ What are the $2-$year and $3-$year forward rates and $\{$:$f_3=\frac{P_2}{P_3}-1)?$

c$.$ Under the expectations hypothesis, what is the expected $1-$year spot interest rate

in year $2?$