In question 34 of the CFAI 2015 AM mock, you are asked to calculate the value of an option using a 2 period binomial model.

The tree starts off with a value of 30, and has a probability of an upmove of 15% per year, and a downmove probability of 20% per year.

Surely this means that to calculate the 1st year value you mutliply 30 by 1.15 for the upmove and 0.8 for the downmove

This gives values of 34.5 and 24. All good so far.

Looking at the solution to the question, the binomial model has these two values for year 1 nodes, however they show year 2 nodes as being 39.675 (uu), 28.75 (ud) and 20.83 (dd).

I agree with the (uu) value as 30 x 1.15 x 1.15 = 39.675

However, unless I am being extremely dumb here, doesnt 30 x 1.15 x 0.8 = 27.6 for the (ud) value? And shouldn’t the (dd) value be 30 x 0.8 x 0.8 = 19.2?

Have I been staring at my screen too long or is this an error?