Actuarial Outpost Annuities Question (ACTEX M2 - 76 #6)
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#1
08-01-2019, 02:31 PM
 Not Paul Member SOA Join Date: Mar 2019 College: St. Edwards University Posts: 132
Annuities Question (ACTEX M2 - 76 #6)

The problem

To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years. The annual effective rate of interest is i. You are given (1+i)^n = 2. Determine i.

My timeline

Let a = 98 and b = 196

------a---a---a----------a----b------b-----------b------0--------0-----------0---
-0---1---2---3--- ... ---n---n+1---n+2---...---2n---2n+1---2n+2---...---3n---

My reasoning

A series of payments of 98 is followed by a series of payments of 196. Payments are stopped and everything in the bank earns interest for n years. The accumulated value at the end of 3n years is 8000.

(98s_n + 196s_2n)(1+i)^n = 8000

The actual solution

The solution says payments continue on to the end of 3n years. A series of 98 payments is made for 3n years and a second series of 98 payments begins at n+1 years and continues until the end of 3n years.

98s_3n + 98s_2n = 8000

What I don't understand

Why are payments taking place between 2n and 3n years?

In general I am having a very difficult time setting up problems involving annuities. While I've got a much better handle on the formulas and vocabulary than I did last month I am still coming up short when trying to set up the problems. Any suggestions for tackling annuities in general?
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Last edited by Not Paul; 08-01-2019 at 02:37 PM..
#2
08-01-2019, 05:35 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 9,149

and 196 at the end of each of the next 2n years
#3
08-01-2019, 05:44 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 6,164

Also, you neglected the investment income from years 1 through 2n.
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#4
08-01-2019, 05:48 PM
 Not Paul Member SOA Join Date: Mar 2019 College: St. Edwards University Posts: 132

at the end of each of the next 2n years.

So what your saying is n + 2n = 3n?

Well that's obvious now
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Last edited by Not Paul; 08-01-2019 at 06:34 PM.. Reason: Because frustordom (boredom and frustration)
#5
08-01-2019, 05:50 PM
 Not Paul Member SOA Join Date: Mar 2019 College: St. Edwards University Posts: 132

Quote:
 Originally Posted by Colymbosathon ecplecticos Also, you neglected the investment income from years 1 through 2n.
Can you say a little more, I don't quite see what you mean.
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#6
08-01-2019, 06:54 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 6,164

8000 = 96s_n*(1+i)^2n + 192s_2n = 96s_3n + 96s_2n (Evaluation at time t=3n)
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