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:

${?}_1{R}_1=9\%,E{(}_2{r}_1)=10\%,E{(}_3{r}_1)=10\mathrm{.}60\%,E{(}_4{r}_1)=10\mathrm{.}95\%$

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

securities$.$

Note: Round your percentage answers to $2$ decimal places $($i$.$e$.,0\mathrm{.}1234$ should be entered as $12\mathrm{.}34).$