Problem $7.$ Suppose the current yield curve looks like the following:

$($a$)$ What is the implied forward rate over the second year, $f_{1,2}?$

$($b$)$ Write down the total return $($per dollar of investment$)$ for two strategies: $($i$)$ Locking

up in a three$-$year "long$-$term" bond; and $($ii$)$ Investing in a two$-$year "medium$-$term" bond

and rolling over with a one$-$year bond over the third year. What is the forward rate over the

third year, $f_{2,3},$ that equalizes the total returns of the above two investment strategies?

$($c$)$ Under the expectations hypothesis, what does the yield curve predict about the path of

short$-$term $($one$-$year$)$ interest rates?