Binomial Interest Rate Tree at expiration

CFA Level II
#1

If I’m doing a calculation for the price of a 5% annual pay 3 year bond, let’s say, and I am given the interest rates (both upper and lower) for Years 1, 2, and 3. Would there ever be a time that I’m discounting the bond in its final year?

Is my first step to discount the $105 back @ the rate that existed in Year 2? Or do I first begin by discounting the bond @ the rate given for Year 3? There was a question in one of the Schweser mocks that threw me off and I can’t seem to find it at this moment. I believe they give me additional information and I fell for it, so I’m looking for a bit of clarity here.

Additional disclosure, I understand the process of combining the two nodes, averaging them out and discounting them back, I just want to be sure about the bond @ maturity in particular. Thanks

#2

You use the rate at time 0 to discount the payments at time 1.

You use the rates at time 1 to discount the payments at time 2.

And so on.

If it’s a 3-year bond, you’ll never use the rates at time 3.

#3

Hmm, so they tricked me.

I would ultimately discount back the cash flow @ maturity back to the discount given for Time 2, correct? I’m about 99% I am correct, but I’d just like peace of mind

#4

Correct.

#5

Thank you kindly Bill

#6

My pleasure.