Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Exam 2/FM - Financial Mathematics
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

DW Simpson Global Actuarial & Analytcs Recruitment
Download our 2017 Actuarial Salary Survey
now with state-by-state salary information!


Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 07-01-2018, 01:08 PM
actsci123451 actsci123451 is offline
SOA
 
Join Date: Feb 2018
Posts: 8
Default Decreasing annuity problem

Francois purchases a 10-year annuity-immediate with annual payments of 10X.

Jacques purchases a 10-year decreasing annuity-immediate which also makes annual payments. The payment at the end of year 1 is equal to 50. At the end of year 2, and at the end of each year through year 10, each subsequent payment is reduced over what was paid in the previous year by an amount equal to X.

At an annual effective interest rate of 7.072%, both annuities have the same present value.

Calculate X, where X < 5.
Answer: 3.59

Can someone please explain why you can't use the decreasing annuity formula ( [n- a-angle-n] /i ) to solve this?
I did 10X a-angle-10 = X(Da)-angle-10 at 7.072%

And when in general can you use the decreasing annuity formula and when can you not?
Reply With Quote
  #2  
Old 07-01-2018, 01:23 PM
Academic Actuary Academic Actuary is offline
Member
 
Join Date: Sep 2009
Posts: 7,795
Default

The payments under the stated decreasing annuity, are 50, 50-X, .........., 50 -9X, while to use the standard decreasing annuity formula X would have to be 5. Use the more general P,Q formula with P = 50 and Q = -5.
Reply With Quote
  #3  
Old 07-01-2018, 03:18 PM
actsci123451 actsci123451 is offline
SOA
 
Join Date: Feb 2018
Posts: 8
Default

Thanks for the reply. So you can only use the DA formula when the payments decrease by a constant amount?
But aren't the payments here decreasing by a constant amount, X, each year? Im still not understanding why I can't do X (Da)angle n.
Reply With Quote
  #4  
Old 07-01-2018, 03:56 PM
Academic Actuary Academic Actuary is offline
Member
 
Join Date: Sep 2009
Posts: 7,795
Default

Quote:
Originally Posted by actsci123451 View Post
Thanks for the reply. So you can only use the DA formula when the payments decrease by a constant amount?
But aren't the payments here decreasing by a constant amount, X, each year? Im still not understanding why I can't do X (Da)angle n.
the Da formula without a leading coefficient is the pattern n, n-1, n-2,...,1. This can be scaled with a multiple. You are really better off never using the Da, and Ia formulas and just using the P,Q formula. Da angle n is P = n, Q=-1. The P,Q formula can be adapted to any arithmetic sequence and any number of payments..
Reply With Quote
  #5  
Old 07-01-2018, 05:54 PM
actsci123451 actsci123451 is offline
SOA
 
Join Date: Feb 2018
Posts: 8
Default

I see, so you can only use DA when in the form n, n-1, ...1. Thanks!
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 08:46 AM.


Powered by vBulletin®
Copyright ©2000 - 2018, 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 0.13927 seconds with 11 queries