Explain the logic behind the answer

CFA Level II
#1

A newly issued zero-coupon bond with a 5-year maturity issued at a price of $71.30 ($100.00 face value) with a yield to maturity of 7.00%. Current US Treasury spot rates and extrapolated forward rates are provided in following table. Bird expects that the future path of interest rates will follow that which is implied by the forward curve.

SPOT AND FORWARD INTEREST RATES

**Maturity (Years)**Spot Rates

Forward Rates (1 year)

(n – 1 years forward)

Forward Rates (n – 1 year)

(1 year forward)

(n)r(n)f(n – 1,1)****f(1,n – 1) 1 3.00% 3.00% 3.00% 2 4.00% 5.01% 5.01% 3 5.00% 7.03% 6.01% 4 6.00% 9.06% 7.02% 5 7.00% 11.10% 8.02%

Q. Using the information provided in Exhibit 1 and assuming that Bird’s interest rate expectation materializes, the forward rate at which an investor would be indifferent to purchasing the US Treasury zero coupon note today or one year from today is closest to:

  1. 8.02%.
  2. 7.02%.
  3. 11.10%.

Why is the answer 8.02%, please explain the logic behind that

#2

bumping up for an answer.

** Is it because one year from now, the forward rates became my spot rates and my discount rate at year 4 is 8.02%?

#3

if you invest at t=0, the bond appreciates at 1.07^5 (spot rates at year 5) - the problem assumes the bond is HTM

if instead the bond is bought an year later (t=1), then two things happen (1) the bond already appreciated 3% (spot rate year 1) and (2) it needs a diff forward rate for the remaining period at time t=1. Hence: 1.03*(1+x)^4=1.07^5 is the equation we need to find the answer

Please note that this is actually already calculated in column 3. Hope that helps