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:

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$.,\backslash (0\mathrm{.}12\backslash \%\backslash )).$ 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$.,\backslash (0\mathrm{.}12\backslash \%\backslash )).$ 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.