CT 5, chapter 9, section 4.4 epv of reversionary annuities depending on term

[Nolasko]

This section is driving me crazy. Can anyone please guide me on how we can derive a final formula without having to derive it from the integral?

I'm attempting question 9.22 and it's solution doesn't make sense to me. Someone please help!!

 

[Robert Chadburn]

These questions are tricky. I'm assuming it's the first bit of the solution that you can't understand? A good approach with any EPV is to calculate:
EPV = sum of {amount}x{discount}x{probability}
Have a look at the attached where I've done this approach. Let me know if this doesn't make sense, or if it was another part of the solution that was the problem. (Note it helps to say exactly which bit or bits of a solution you need help with).

 

[Nolasko]

This helps a lot. Thank you!

These questions are tricky. I'm assuming it's the first bit of the solution that you can't understand? A good approach with any EPV is to calculate:
EPV = sum of {amount}x{discount}x{probability}
Have a look at the attached where I've done this approach. Let me know if this doesn't make sense, or if it was another part of the solution that was the problem. (Note it helps to say exactly which bit or bits of a solution you need help with).