Problem $1$ Suppose you are given the following information about the default$-$free,

coupon$-$paying yield curve:

a$)$ Determine the yield to maturity of a two$-$year zero$-$coupon bond.

b$)$ What is the zero$-$coupon yield curve for years $1$ through $4?$

c$)$ What is the forward rate for year $3($short rate from end of year $2$ until end of year

$3$

d$)$ What is the forward rate for year $4($short rate from end of year $3$ until end of year

$4$

e$)$ Now suppose that the forward rate for year $4$ suddenly changes and becomes equal

to the forward rate for year $3($the one that you calculated in part $($c$)).$ What will

be the new zero$-$coupon spot rate for a $4-$year investment?