The following table shows the current prices for zero$-$coupon bonds with different maturities as of January $1,2018.$ The bonds are identical in every respect except for the time to maturity. All of the bonds will be redeemed at their par value of $100$ upon redemption.

Term to Maturity $($year$)1234510$

Spot Price $()96\mathrm{.}6291\mathrm{.}5786\mathrm{.}3880\mathrm{.}7274\mathrm{.}7352\mathrm{.}77$

$3\mathrm{.}1$

$3\mathrm{.}2$

$3\mathrm{.}3$

B

Compute the yield to maturity $($YTM$)$ for these bonds. Draw the yield curve and briefly discuss how the yield curve describes the implications in terms of the expectations as well as the liquidity preference hypotheses.

$(12\%)$

What are the two important conditions or assumptions behind for you to realize these promised YTM$?$ If these two conditions or assumptions are not met, what kind of risk would you have?

$(5\%)$

Compute the implied forward two$-$year rate of interest at January $1,2021.$ Describe the conditions under which the calculated forward rate would be an unbiased estimate of the two$-$year spot rate of interest at January $1,2021.$