Example: Suppose that $r_0=0\mathrm{.}05.$ The current price of a risky asse is $p_t=R12\mathrm{.}50.$ There are three possible states of the world in peri $t+1.$ The state$-$contingent payoffs $($or payoff distribution$)$ of the asset are summarised below:

$\backslash$table$[[$State$-$contingent asset payoffs$],[$State$,1,2,3],[$Probability$,0\mathrm{.}3,0\mathrm{.}5,0\mathrm{.}2],[$Payoff$,13\mathrm{.}75,12\mathrm{.}75,14\mathrm{.}5]]$

Calculate the risk$-$free payoff on investing $R12\mathrm{.}50.$ Calculate the expected payoff associated with investing in one unit of the risky asset.

$$ Determine the expected risk premium on the asset.