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


Not looking for a job? Tell us about your ideal job,
and we'll only contact you when it opens up.
https://www.dwsimpson.com/register


Long-Term Actuarial Math Old Exam MLC Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #11  
Old 09-17-2018, 01:24 PM
windsowe windsowe is offline
Member
SOA
 
Join Date: Feb 2011
Location: Nashville
Studying for LTAM
College: Vanderbilt Alum
Favorite beer: Hopothermia Double IPA
Posts: 217
Default

It's 6.3 from the LTAM 165:

Stuart, now age 65, purchased a 20-year deferred whole life annuity-due of 1 per year at age 45.
You are given:
(i) Equal annual premiums, determined using the equivalence principle, were paid
at the beginning of each year during the deferral period.
(ii) Mortality at ages 65 and older follows the Standard Ultimate Life Table.
(iii) i = 0.05
(iv) Y is the present value random variable at age 65 for Stuart’s annuity benefits.
Calculate the probability that Y is less than the actuarial accumulated value of Stuart’s
premiums.
Reply With Quote
  #12  
Old 09-17-2018, 01:27 PM
Academic Actuary Academic Actuary is offline
Member
 
Join Date: Sep 2009
Posts: 9,194
Default

Quote:
Originally Posted by windsowe View Post
I have a question about curtate future lifetime. In question 6.3 of the LTAM MC 165, why do we had 1 to the curtate future lifetime of the 65 year old? Why wouldn't the probablility involved simply a:K(t) of a 65 year old instead of a:K(t)+1 of a 65 year old? Thanks for your help!
Because its an annuity due.
Reply With Quote
  #13  
Old 09-17-2018, 01:30 PM
windsowe windsowe is offline
Member
SOA
 
Join Date: Feb 2011
Location: Nashville
Studying for LTAM
College: Vanderbilt Alum
Favorite beer: Hopothermia Double IPA
Posts: 217
Default

Ah---that helps a lot!
__________________

___________
P FM MFE C LTAM PA
FNCE ECON STAT

FAP: 1 2 3 4 5 IA 6 7 8 FA
APC
Reply With Quote
  #14  
Old 09-17-2018, 01:34 PM
Jim Daniel's Avatar
Jim Daniel Jim Daniel is offline
Member
SOA
 
Join Date: Jan 2002
Location: Davis, CA
College: Wabash College B.A. 1962, Stanford Ph.D. 1965
Posts: 2,728
Default

Quote:
Originally Posted by windsowe View Post
I have a question about curtate future lifetime. In question 6.3 of the LTAM MC 165, why do we had 1 to the curtate future lifetime of the 65 year old? Why wouldn't the probablility involved simply a:K(t) of a 65 year old instead of a:K(t)+1 of a 65 year old? Thanks for your help!
Count how many payments are made, depending on K. If K = 0, for example, so that T=0.xxx, then 1 payment was made. And 1 = 0 + 1. In general, K+1 payments are made.
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
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 09:23 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 0.13555 seconds with 9 queries