Binomial Valuation of bonds: With Semi-annual coupon?

Ok I just came across a Q in Schweser Pro that freaked me out, or maybe I just didn’t comprehend this model properly. When the coupon is paid semi-annual, why do we add only half of the annual coupon to each node? For example: Bond that pays 5% semi-annual coupon --> each year it should pay $5 (2 6 month coupon payments of $2.5), but in the solution it assumes: At year 2: $100 + $2.5 and discount at [year 1 discount rate / 2] 1) why do we assume the bond pays a coupon of only $2.5 in a year? 2) why do we discount at rate/2? thanks.

because at T = 2 you just get 2.5 bucks T = 0 you get 0 T = .5 you get 2.5 T = 1 you get 2.5 T = 1.5 you get 2.5 T= 2 you get 2.5 T = 2.5 you get 2.5… etc etc

It is may be because question has asked us to calculate the bond value which has semi-annual payments through binomial model. Also if we are taking half coupon then discount rate should be half. Am I Missing Anything?

Ok here’s the wording of the Q: Using the following tree of semiannual interest rates what is the value of a 5% callable bond that has one year remaining to maturity, a call price of 99 and pays coupons semiannually? so T2 would be one year form now T1 would be 6 months from now Right?

coupon of 5% means you get paid $2.5 twice a year.

it clearly says paying semiannually

Each node is only 6 months long, so you use $2.50 as a coupon payment and you only discount it back 6 months (i.e. 1/2 the interest rate).