You observe that the current three-year discount factor for default-risk free cash flows is 0.68. Remember, the t-year discount factor is the present value of $1 paid at time t, i.e. = (1 + ), where is the t-year spot interest rate (annual compounding). Assume all bonds have a face value of $100 and that all securities are default-risk free. All cash flows occur at the end of the year to which they relate.

a) What is the price of a zero-coupon bond maturing in exactly 3 years?

b) Your friend makes the following observation about the above bond: Since there is no risk of default and there are no coupons to re-invest, buying the 3-year zero coupon bond today is a risk-free investment; that is, you are guaranteed to earn an annual return of 13.72% (i.e. 3-year spot rate). Explain why your friend is not entirely correct and how you would modify the statement to make it correct.