Problem $6-13$ Unbiased Expectations Theory $($LG$6-7)$

Suppose we observe the following rates: ${?}_1{R}_1=8\%,{?}_1{R}_2=10\%.$ If the unbiased expectations theory of the term structure of interest rates holds, what is the $1-$year interest rate expected one year from now, $E{(}_2{r}_1)?$

Note: Do not round intermediate calculations. Round your percentage answer to $2$ decimal places $($i$.$e$.,0\mathrm{.}1234$ should be entered as $12\mathrm{.}34).$

Answer is complete but not entirely correct.

$10\mathrm{.}00ox\%$