Assume that the pure expectations theory of the term structure is correct. $($This implies that you can use the yield curve provided to $$back out$$ the market$$s expectations about future interest rates.$)$ What does the market expect will be the interest rate on $1-$year securities one year from now? What does the market expect will be the interest rate on $3-$year securities two years from now? Calculate the yields using geometric averages. $(1+$ r$2)2=((1+$ r$1)$ x $(1+1$r$1)1\mathrm{.}1278=(1\mathrm{.}0600$ x $(1+1$r$1)1$r$1=(1+$ r$5)5=((1+$ r$2)2$ x $(1+2$r$3)31\mathrm{.}3701=(1\mathrm{.}1278$ x $(1+2$r$3)32$r$3=$