Question $4(15$ marks$)$

There are two types of bonds available in the market: a $4-$year bond A with annually paid

coupon rate of $30\%$ selling at a yield to maturity of $30\%.$ and a $4-$year zero$-$coupon bond B

setling at a yield to maturity of $30\%.$ Both types have a par value of $$1,000$ and assume that

the number of the bonds can be sold in proportional to the dollar amounts invested. Answer

the following questions based on the information above.

a$)$ What is the duration for the $4-$year coupon bond A$?(5$ marks$)4$

b$)$ Suppose that you want to choose either bond $A$ or bond $B,$ to invest for $3$ years. If you

expect that the discount rate may be $25\%$ for the following five years after your

purchase, which bond is a better investment choice? Compare their effective

annualized returns. $(5$ marks$)$

c$)$ Suppose that you now manage a pension fund for $$1,000$ that will provide retired

workers a guaranteed investment contract $($GIC$)$ with $3-$year maturity, and a

guaranteed interest rate of $30\%.$ As you expect that there will be uncertainty in the

future discount rate, how do you invest in bond A and$/$or bond $B$ to fund and

immunize the obligation? Assume that the discount rate is $35\%$ for the following five

years after your investment, validate the immunization by comparing the accumulated

value of your investment with your obligation at maturity. $(5$ marks$)$