Math Questions:

Question $12(10$ pts$).$ If you note the following yield curve

in The Wall Street Journal, what are the one$-$year future

rates for the periods beginning one year and two years from

today $($that is$,E{(}_2{r}_1)$ and $E{(}_3{r}_1)),$ according to the unbiased

expectations theory? Round your percentage answer to $2$

decimal places. $($e$.$g$.,0\mathrm{.}12\%).$ Show your calculation

steps to receive full credits.

Question $13.$ Based on economists' forecasts and analysis,

the spot and future one$-$year Treasury bill rates and

liquidity premiums for the next two years are as follows:

R

E$(2$r

E$(3$ r

a$.(10$ pts$)$ According to the unbiased expectation

theory, calculate the current yield to maturity for $1)$

two$-$year and $2)$ three$-$year Treasury securities$.$

Round your percentage answers to $2$ decimal

places. $($e$.$g$.,0\mathrm{.}12\%).$ Show your calculation steps

to receive full credits.

b$.(10$ pts $)$ According to the liquidity premium theory,

calculate the current yield to maturity for $1)$ two$-$

year and $2)$ three$-$year Treasury securities$.$ Round

your percentage answers to $2$ decimal places.

$($e$.$g$.,0\mathrm{.}12\%).$ Show your calculation steps to

receive full credits.

c$.($Extra credit: $15$ pts$)$ Based on your results, draw

the yield curve under each theory in one graph.

Compare and briefly discuss the shapes of the two

curves.