Problem $2-8($LG $2-7)$

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

years $2,3,$ and $4,$ respectively$)$ are as follows:

${?}_1{R}_1=0\mathrm{.}3\%,E{(}_2{r}_1)=1\mathrm{.}3\%,E(3r_1)=9\mathrm{.}4\%,E(4r_1)=9\mathrm{.}75\%$

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

securities$.($Round your percentage answers to $3$ decimal places. $($e$.$g$.,32\mathrm{.}161))$