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Recall that a zero-coupon bond, also called a pure discount bond and sometimes known as a ”zero”, pays no principal or interest until maturity

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Recall that a zero-coupon bond, also called a pure discount bond and sometimes known as a ”zero”, pays no principal or interest until maturity. A ”zero” has a par value or face value, which is the payment made to the bondholder at maturity. The zero sells for less than the par value, which is the reason it is a discount bond. This problem studies the relation between a zero price with the interest rate movement. Let’s consider a 20-year zero value of $1,000 and 6% interest compounded semiannually. a. What is the fair price of this zero coupon bond at time 0? b. Suppose that you bought the zero for the amount that you just computed in part (a.) at time zero, and then six months later the interest rate increases to 7%. What will be the fair price at time o.s? If you sell the bond at t = 0.5, what is your return per year? (Hint: A return is defined as Profit or Loss /Initial investment. Notice that for this question, the investment horizon is just o.s year.) c. What conclusion can you draw from the above example on the relation between a zero price with the under- lying interest rate? What is your intuition?