I completely understand the calculations used in the binomial interest rate tree but I believe that backward induction starts at the very back of the tree. However, in the solution, they started at year 2, any reason why they skipped year 3 completely?

because the bond matures in year 3. So you know you will receive par + coupon

So you just completely ignore and skip the year in which the bond matures?

the way I look at it, is you always use the interest rate prior to the year as your discount rate (6.9% for cash flows expected in year 3 for the top node) So, the rates listed in year 3 would only be used to discount any cash flows from year 4, which as per my previous comment would be non-existent. Hope this helps

haha, i had the same question earlier this morning. i completely missed that the bond matures on Year 3, so you use the rates from Y2 and Y1 to get to today. if the bond matured in Year 4, then you would use the rates in Y3, Y2 and Y1 to get to today.