Question $1$

Suppose that we live in a market where we have the following bonds:

$($a$)(")$ Determine the term structure of interest rates in this economy by computing the

spot rates $r_1,r_2,$ and $r_3.$

$($Use at least three decimals for intermediate calculations. Write your final answers in

percentage and round to one decimal: for instance, if the answer is $3\mathrm{.}45\%$ or $3\mathrm{.}47\%,$

write $3\mathrm{.}5$ without the percentage sign; if the answer is $3\mathrm{.}44\%$ or $3\mathrm{.}42\%,$ write $3\mathrm{.}4.)$

The $1-$year spot rate $r_1$ is:

$\%$

The $2-$year spot rate $r_2$ is:

$\%$

The $3-$year spot rate $r_3$ is

$\%$

$($b$)(")$ What are the forward rates in this economy? In particular, spell out what rate you

can get for an investment in year $1$ that matures in year $2(f_{1,2}),$and for an investment in

year $2$ that matures in year $3(f_{2,3}).$

$($Use at least three decimals for intermediate calculations. Write your final answers in

percentage and round to one decimal: for instance, if the answer is $3\mathrm{.}45\%$ or $3\mathrm{.}47\%,$

write $3\mathrm{.}5$ without the percentage sign; if the answer is $3\mathrm{.}44\%$ or $3\mathrm{.}42\%,$ write $3\mathrm{.}4.)$

The forward rate $f_{1,2}$ is:

$\%$

The forward rate $f_{2,3}$ is:

$\%$

$($c$)(")$ Compute the yields$-$to$-$maturity $($ytm$)$ of the three bonds: $y_A$ for Bond $A,y_B$ for

Bond B $,$ and $y_C$ for Bond C $.$

$($Use at least three decimals for intermediate calculations. Write your final answers in

percentage and round to one decimal: for instance, if the answer is $3\mathrm{.}45\%$ or $3\mathrm{.}47\%,$

write $3\mathrm{.}5$ without the percentage sign; if the answer is $3\mathrm{.}44\%$ or $3\mathrm{.}42\%,$ write $3\mathrm{.}4.)$

The ytm of Bond $A{y}_A$ is:

$\%$

The ytm of Bond $B{y}_B$ is:

$\%$

The ytm of Bond $C{y}_O$ is:

$\%$