It is often said that inverted yield curves $($with long$-$term yields lower than shortterm yields$)$ forecast upcoming recessions. Let's think through the logic of it$.$

For simplicity, just consider one and two$-$year bonds. Their annual bond yields are given by ${?}_1{R}_1$ and ${?}_1{R}_2,$ respeetively. Let $E{(}_2{r}_1)$ denote the current market expectation fo the one$-$year interest rate next year. To avoid confusion, the timing span over which these interest rate variables operate are drawn in the Figure below.

$($a$)(2$ points$)$ Suppose ${?}_1{R}_2=4\%$ and ${?}_1{R}_1=5\%.$ Assume that unbiased expectation hypothesis is true. What is $E{(}_2{r}_1)?($Please show the process of numerically solving for it$.)$