Problem $6-5$ Unbiased Expectations Theory $($LG$6-7)$

Suppose that the current $1-$year rate $(1-$year spot rate$)$ and expected $1-$year T$-$bill rates over the following three years $($i$.$e$.,$ years $2,3,$

and $4,$ respectively$)$ are as follows:

${?}^1{R}_1=6\%,E(2r_1)=7\%,E(3r_1)=7\mathrm{.}70\%,E(4r_1)=8\mathrm{.}05\%$

Using the unbiased expectations theory, calculate the current $($long$-$term$)$ rates for one$-,$ two$-,$ three$-,$ and four$-$year$-$maturity Treasury

securities$.($Round your answers to $2$ decimal places.$)$