Problem $1$ Suppose you are given the following information about the default$-$free, coupon$-$paying yield curve:

Maturity $($years$)$

Coupon Rate $($annual payments$)$ YTM

$12340\mathrm{.}00\%10\mathrm{.}00\%12\mathrm{.}00\%4\mathrm{.}00\%2\mathrm{.}000\%3\mathrm{.}908\%6\mathrm{.}597\%6\mathrm{.}878\%$

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 $4?$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?

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?