Binominal option pricing, do we ever need the interest rate for the last year?

[Jones473]

It seems we never need the possible interest rates in the tree if we are valuing a zero or fixed coupon bond. E.g. to value a 3Y fixed or zero coupon bond, we only need to calculate the interest rate tree for 2 years?
Am I right that we only need the interest rates for the 3 year if there is any embedded options?

 

[S2000magician]

Whether there are embedded options or not, if you have a bond that matures in n periods, your tree need go only out to time n − 1.
You still have n periods of discount rates, but they’re at times 0, 1, …, n − 1, not at times 1, 2, …, n.