Please write explanations for your calculations, do not just submit the answer. These do not need to be very long; rather concisely explain what you are doing.
Bond VALUATIONS
In the problems below, all coupon and yield rates are quoted as nominal rates payable semiannually (so $\mathrm{r}^{(2)}$ and $j^{(2)}$ respectively). Use the following convention: the issue date is $\mathrm{t}=0$ and the first coupon payment occurs at $t=1 ; t$ is measured in $\frac{1}{2}$ ‘s of a year. If not specified otherwise, $P$ refers to the price of the bond at the issue date $t=0$.
Also recall the formulas for finding the bond price $P$ at the end of Lecture 11 .
Problem 1. Calculate the price P (at the issue date) of a 10-year bond with face value $\$ 100$, coupon rate $5 \%$ and a yield rate $7.2 \%$.

Problem 2. The fair price of the bond at the issue date is $P=\$ 95$. This is an 8-year bond, whose face value is $\$ 100$ and the coupon rate is $4 \%$. Find the nominal semiannual yield rate $j^{(2)}$ for this bond.

Problem 3. Consider a bond $A$ maturing in 8 years and having the face value of $\$ 100$, coupon rate of $5 \%$ and the yield rate of $6 \%$.
(a) Find the current fair price $P$ of bond $A$.
Now consider bond B that has the same current fair price, maturity and the coupon rate as bond A above.
(b) If bond $B$ has the yield rate of $7 \%$, what is the face value of bond $B$ ?
Problem 4. Bond A has face value of $\$ 100$, coupon rate of $4.75 \%$ and current fair price $P=\$ 85.16$. Bond B has face value of $\$ 100$, coupon rate of $6.25 \%$ and the current fair price of \$95.05. Both bonds have the same yield rates and the same terms (time to maturity). Find the nominal yield rate and the term for both bonds.

Hint: you will have two equations (price of bonds A and B) with two unknowns (yield rate and the time to maturity).

Problem 5. Consider a bond with face value $\$ 1000$, coupon rate $5 \%$, yield rate $10 \%$, maturing in 10 years. Note that this means there will be 20 coupon payments.
(a) Find the price at the issue date $\mathrm{P}(\mathrm{t}=0)$.
(b) Find the price right after the second coupon has been paid:
$\mathrm{P}(\mathrm{t}=2 ;$ after the coupon payment $)$.
(c) Find the price right before the second coupon payment:
$\mathrm{P}(\mathrm{t}=2$; right before the coupon payment $)$.
(d) Find the price 3 month after the 6 -th coupon payment:
$$
\mathrm{P}\left(\mathrm{t}=6 \frac{1}{2}\right) \text {. }
$$
(e) Find the price 1 month before the 8-th coupon payment. (Figure out the value of t yourself).