Consider investing in a US Treasury bond with a $1,000 par value and 5% coupon rate. Coupons are paid semiannually and the next payment is exactly six months away. Suppose the bond has 3 years to maturity.
a. What is the price of the bond if the market interest rate, at that maturity, is 5%?
b. Suppose that you have purchased the bond, and the next day the market interest rate on similar bonds falls to 4%. What will the price of your bond be now?
c. Now suppose that one year has gone by since you bought the bond, and you have received the first two coupon payments. How much would another investor be willing to pay for the bond? What was your total return on the bond? If another investor had bought the bond a year ago for the amount that you calculated in (b), what would that investor’s total return have been?
d. Now suppose that two years have gone by since you bought the bond and that you have received the first four coupon payments. At this point, the market interest rate on similar bonds unexpectedly rises to 7%. How much would another investor be willing to pay for your bond? Suppose that another investor had bought the bond at the price you calculated in (c). What would that investor’s total return have been over the past year?