The current interest rates $($at time t$)$ on one through five year bonds are $1\%,3\%,5\%,7\%$ and $9\%.$

a$)$ Assuming no liquidity premia, what are the expected future rates on $1$ year bonds out to t $+4?$

b$)$ What are the implied liquidity premia $($for two through five year bonds$)$ if interest rates are expected to be stable at their current structure?

c$)$ Assume investors are concerned about future defaults on bonds, and there are escalating risk premia of $1\%$ per year of maturity beyond the first year. Assuming the current term structure is stable, what are the implied liquidity premia?

d$)$ The situation in part c$)$ continues into the next year, except that one year bond rates have jumped to $5\%.$ Assuming the risk and liquidity premia are unchanged, what are the expected future rates on $1$ year bonds out to t$+4?$

e$)$ What does the value of i$\_$t$+1^$e suggest about economic performance in the next year?