ASM FM exam question - newest 16th edition Sections 4h-4i, page 201 #21

I’m not sure if I can ask these sorts of questions here but I just signed up with goactuary and I don’t know all the rules yet. If this is not allowed then I apologize.
Can somebody please help me with the algebra for #21… particularly for 21. (I). I see that the answer is true but for some reason can’t get the algebra to work. Any help would be greatly appreciated.

This sort of question shouldn’t be a problem. You’re quoting what appears to be a publicly available Exam question (based on the “[CAS 5/90 #5]”).

So long as you’re not showing proprietary information or copyrighted material, you should be fine.

Sure, you can ask questions like this here. You may get responses, though the preliminary exam forums are less active here than on the old Actuarial Outpost.

Suggestion: it is best if you try to show your work so that people can point out what is wrong. That way they also don’t have to type out things that aren’t part of your difficulty.

Here, I’ll suggest that for I, you would be far better doing it without the algebra. On the left, you have a payments of (1 at time 0; 2 at time 1; …, n at time n-1) + (n at time 0; n-1 at time 1; …; 1 at time n-1). Just grouping them by payment time: (n+1 at time 0; n+1 at time 1; … n+1 at time n-1). So (n+1)S(double dot)n.

For algebra, depends on what formulas you know as starting points.

How about (Is(immed))_n = ((1+i)s(immed)_n - n)/i and (Ds(immed)_n = n(s(immed)_n)-(s(immed)_n - n)/i

(Those from, pages 4-23 and 4-25)

Adding those, Is(immed)+Ds(immed) = s(immed)_n [from the extra +1 in the first expression, which doesn’t cancel] + n(s(immed)_n) = (n+1)s(immed)_n.

Then just multiply immediates by (1+i) to get dues.

Thank you very much gandalf. I sincerely appreciate it.
Is there a different website for the ‘old’ Actuarial Outpost as opposed to

Thank you very much Vorian.

There isn’t. The old ao was shut down and replaced with what’s over there now. All the old posts were removed and not placed back online.

Yes, as SpaceLobster said, what was there is all gone.