An investor is considering a 3-year, 4% annual coupon bond with a face value of $1,000. Current 1-year spot rate is 3.0%, and the 2-year forward rate one year from now (1f1) is 3.5%. The investor anticipates that the 1-year forward rate two years from now (2f1) will be 4.0%. Assuming annual compounding, what is the fair price of the bond?

Correct answer: D. $1,010.34

To find the fair price, we need to discount each cash flow at the appropriate spot rate. First, we need to calculate the 2-year and 3-year spot rates using the given forward rates. 1-year spot rate (z1) = 3.0% 2-year spot rate (z2): (1 + z2)^2 = (1 + z1) * (1 + 1f1) = (1 + 0.03) * (1 + 0.035) = 1.03 * 1.035 = 1.06605. So, z2 = sqrt(1.06605) - 1 = 0.032517 or 3.2517% 3-year spot rate (z3): (1 + z3)^3 = (1 + z2)^2 * (1 + 2f1) = 1.06605 * (1 + 0.04) = 1.06605 * 1.04 = 1.108692. So, z3 = (1.108692)^(1/3) - 1 = 0.035043 or 3.5043% Cash flows: Year 1: $40 coupon Year 2: $40 coupon Year 3: $40 coupon + $1,000 face value = $1,040 Bond Price = $40 / (1 + 0.03) + $40 / (1 + 0.032517)^2 + $1,040 / (1 + 0.035043)^3 Bond Price = $40 / 1.03 + $40 / 1.06605 + $1,040 / 1.108692 Bond Price = 38.83495 + 37.52187 + 938.0772 Bond Price = $1,010.434