Ct5 Chapter 6 Question 6.13

Hello!
I'm a little confused with the question 6.13 on page 28 of chapter 6.
In the question they have mentioned that the policy is subjected to simple reversionary bonus that vest at the START of each year.
Also, it has been stated on page 26 that while calculating the net premium reserve, the total bonus amount includes bonuses added up to and INCLUDING time t.
According to that, we must have 8 bonuses, 600 for the first year and 562.5 for the rest, as we must also include the bonus at the 7th year.

But in the solution, we have accounted for only 7 bonuses.
Please help me with it.
Thanks in advance

 

draw a timeline. Suppose you draw a timeline from 0 to say 3. It has 3 years with the following intervals [0, 1), [1, 2) and [2, 3). Now apply this reasoning to the reversionary bonuses and you will get only 7 bonuses. Timelines help to make the setup clearer. I use it to get a picture of what's going on

 

since its a with profit policy and in with profit policy while calculating the net premium reserve
we take the previously earned bonus and not the future bonus so since you are calculating
reserve at time 7 that means you have survived 7 years so you should take previous
7 bonus which you should add to sum assured. the next bonus and next premium will
vest or received after calculations of reserve. that is why 7 bonus. Reserve is calculated before next bonus
received and next premium received.
so for example if bonus is received on 1 jan so reserve will be calculated on midnight of 31 December
and after the bonus will be vested.