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Question 1.1 of the Annuities Tut for Models

+3 votes
asked May 21, 2016 in BUS 3018F - Models by DanNewton (970 points)

Seems extremely basic, but I can't see any relationship, or find it anywhere on the table. The question is:

1.1 Find the value of \(a_\bar{45:n|} \) on A1967–70 mortality at 6% interest.

Numerical Answer given as 10.914.

1 Answer

+2 votes
answered May 21, 2016 by niall_morley (570 points)
edited May 27, 2016 by niall_morley

Hi Dan, there are a few ways to go about this question. One possible way is:

\({a}_\overline{45:20|} \) = \(\ddot{a}_\overline{45:20|} - 1 +v^{20} \cdot _{20}p_{45}\)

you can break it down further (again all in advance):

\(\ddot{a}_{45}  - v^{20}\ _{20}p_{45}\ddot a_{65} - 1 +v^{20}\ _{20}p_{45}\) 

commented May 21, 2016 by DanNewton (970 points)

Yeah I did that from first principles, didn't come out right... So it's either the answer that's wrong or I'm not reading the tables correctly. Either way, that clarifies the method, thanks :)

commented May 21, 2016 by simon_rigby (4,220 points)

Thanks Niall. I just fixed the notation a bit. It's \ddot{ }

commented May 27, 2016 by jolegutko (870 points)

Thanks both! Should the last annuity factor have a 65 subscript rather than 45? (#rustycontingencies)

commented May 27, 2016 by niall_morley (570 points)

Hi Jo, you are correct, I have adjusted the solution!