Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Financial Mathematics
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

DW Simpson Global Actuarial & Analytics Recruitment
Download our Actuarial Salary Survey
now with state-by-state salary information!


Financial Mathematics Old FM Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 08-01-2019, 02:31 PM
Not Paul Not Paul is offline
Member
SOA
 
Join Date: Mar 2019
College: St. Edwards University
Posts: 132
Default 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?
__________________
Taking a well deserved break. Back at it in some capacity next year.

P FM IFM
VEE: Economics VEE: Accounting VEE: Statistics
Job

Last edited by Not Paul; 08-01-2019 at 02:37 PM..
Reply With Quote
  #2  
Old 08-01-2019, 05:35 PM
Academic Actuary Academic Actuary is offline
Member
 
Join Date: Sep 2009
Posts: 9,149
Default

and 196 at the end of each of the next 2n years
Reply With Quote
  #3  
Old 08-01-2019, 05:44 PM
Colymbosathon ecplecticos's Avatar
Colymbosathon ecplecticos Colymbosathon ecplecticos is offline
Member
 
Join Date: Dec 2003
Posts: 6,164
Default

Also, you neglected the investment income from years 1 through 2n.
__________________
"What do you mean I don't have the prerequisites for this class? I've failed it twice before!"


"I think that probably clarifies things pretty good by itself."

"I understand health care now especially very well."
Reply With Quote
  #4  
Old 08-01-2019, 05:48 PM
Not Paul Not Paul is offline
Member
SOA
 
Join Date: Mar 2019
College: St. Edwards University
Posts: 132
Default

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

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

Well that's obvious now
__________________
Taking a well deserved break. Back at it in some capacity next year.

P FM IFM
VEE: Economics VEE: Accounting VEE: Statistics
Job

Last edited by Not Paul; 08-01-2019 at 06:34 PM.. Reason: Because frustordom (boredom and frustration)
Reply With Quote
  #5  
Old 08-01-2019, 05:50 PM
Not Paul Not Paul is offline
Member
SOA
 
Join Date: Mar 2019
College: St. Edwards University
Posts: 132
Default

Quote:
Originally Posted by Colymbosathon ecplecticos View Post
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.
__________________
Taking a well deserved break. Back at it in some capacity next year.

P FM IFM
VEE: Economics VEE: Accounting VEE: Statistics
Job
Reply With Quote
  #6  
Old 08-01-2019, 06:54 PM
Colymbosathon ecplecticos's Avatar
Colymbosathon ecplecticos Colymbosathon ecplecticos is offline
Member
 
Join Date: Dec 2003
Posts: 6,164
Default

8000 = 96s_n*(1+i)^2n + 192s_2n = 96s_3n + 96s_2n (Evaluation at time t=3n)
__________________
"What do you mean I don't have the prerequisites for this class? I've failed it twice before!"


"I think that probably clarifies things pretty good by itself."

"I understand health care now especially very well."
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 12:58 AM.


Powered by vBulletin®
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.24153 seconds with 11 queries