Why does the solution trend forward the AIY/EE using the result from YR 2013 of 312.5? Would it be as appropriate to select the YR 2012 value of 306 and then trend forward at 2% an additional year (i.e. 3 and 4 years versus 2 and 3 years).
Building on that, we are trending to future average accident dates of 7/1/15 and 7/1/16 as a part of that calculation, so when compared to the future average accident date of the effective period of 1/1/16, we can apply 0.5 to each of the 2015 and 2016 projected AIY/EE or take the straight average because 1/1/16 is right in the middle of those two dates?
For the first part of your question: Yes, you could trend 3 and 4 years from 2012 then take the average and you would get, 327.98, very close to the sample answer, where I’m again taking the straight average like in the sample solution. But it’s generally preferable to use the most recent data because it’s likely more credible and because the trend period is smaller so projection errors are minimized. (In this case, the selected trend is only 2% so the difference between your method and the sample answer is small anyway.)
For the second part of your question: Yes, your approach of trending 2015 forward by 0.5 years, and 2016 backwards by 0.5 years is probably more accurate. The solution takes the simple average as an approximation but because the trend periods of 0.5 years are so small, and the trend of 2% is so small, the difference between your suggested method and the sample answer is again small. You would not lose points if you used your trending method here instead of taking the average - you just might save a little time on the exam.