Rates of return and forward rates:

Consider investment in three T$-$bonds. The first T$-$bond matures in six months, has an

annualized coupon rate of $23$

$8$

and trades at $99$ : $8.$ The second T$-$bond bond matures in $12$

months, has an annualized coupon rate of $37$

$8$

and trades at $99$ : $2.$ The third T$-$bond bond

matures in $18$ months, has an annualized coupon rate of $41$

$8$

and trades at $99$ : $24\mathrm{.}1$ Use the

Law of One Price to calculate discount factors, spot rates, and the forward rates $1$f$1$ and $2$f$1.$

Now, assume that you hold all three bonds until time $2$ and that you enter agreements to

sell bonds not yet matured at their forward prices and to reinvest all interim cash flows,

including those of bonds that reach maturity, at the current forward rates.

Calculate the rates of return from investing in each of the three bonds.