Need help in understanding the selling price calculation

“An investor buys a four-year, 10% annual coupon payment bond priced to yield 5.00%. The investor plans to sell the bond in two years once the second coupon payment is received. Calculate the purchase price for the bond and the horizon yield assuming that the coupon reinvestment rate after the bond purchase and the yield-to-maturity at the time of sale are (1) 3.00%”, CFAI Book pg 536

a) while calculating the price at which the bond was sold when I use 

       N=2, PV=-117.72, IY = 3, PMT = 10 I get a FV of 104 

b) were as the correct method to calculate the selling price after 2 years is a DCF:

     10/(1.03)^1+ 110/(1.03)^2 = 113.39.

Why is the selling price calculated as DCF? what am I missing when I try to calculate the selling price as in example (a).