Why are these two BONDS questions answered differently?

CFA Level II
#1
  1. Given the following relevant part of the interest rate tree, the value of the callable bond at node A is closest to: Annual coupon 6.25% Corresponding part of the callable bond tree: $100.00 A ====> - $100.00 ----3.44% 3.15% ----2.77% The value of the bond at node A is closest to: A) $101.53. B) $100.00. C) $103.56 Bond Value at node A = the lesser of either $100 or {0.5 × [$100.00 + $6.25/2] + 0.5 × [$100.00+ $6.25/2]}/(1+ 3.15%/2) = $101.52. Since the call price of $100 is less than the computed value of $101.52 the bond price would be $100 because once the price of the bond reached this value it would be called. ---->>*****Notice: they divide by (1+3.15%/2) ***************<> in this example they divide by (1.0759%/2), the lower and upper rates, not the first rate as in the example above ***** <
#2

I believe that in the 2nd question, “node A” refers to the point where the (semiannual) interest rate is 7.59%, which is different from question 1, where it seems to be the origin of the interest rate tree. We have a bond that has 1 year to maturity, we know the coupon, and we know the interest rate for the first half year, and two possible rates for the second half year. The formula you cite will give you the value of the bond after 6 months, assuming the interest rate went up. Of course, you’re not done yet - you need to do the same thing again, assuming interest rates went down: Vdown,6mths = min( (102.5/(1 + 0.0533/2)), 99) = min (99.83, 99) = 99. Now we can compute the value at the tree node: V_0 = min( (0.5 x (98.75+2.5) + 0.5 x (99+2.5) )/(1+0.0635/2), 99) = 98.26 ====> Answer C.

#3

Naze, thanks for responding. You are exactly correct. That is very difficult stuff. It took me an hour of just blank stares, but I did get it. What I don’t understand (but i will soon hopefully) is why sometimes “node A” refers to the point where the (semiannual) interest rate is 7.59%, which is different from question 1, where it seems to be the origin of the interest rate tree." Perhaps something to do with: “has one year remaining to maturity” vs. another example “will mature in two years at par value”