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
Actuarial Jobs

Visit our site for the most up to date jobs for actuaries.

Actuarial Salary Surveys
Property & Casualty, Health, Life, Pension and Non-Tradtional Jobs.

Actuarial Meeting Schedule
Browse this year's meetings and which recruiters will attend.

Contact DW Simpson
Have a question?
Let's talk.
You'll be glad you did.


Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 03-17-2018, 01:09 PM
Nagsinde2002 Nagsinde2002 is offline
SOA
 
Join Date: May 2017
College: University of Wisconsin - Madison (1st year)
Posts: 13
Default Prospective and Retrospective Methods Question

Hello, I was looking at Example 37.2 from "A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2" by Marcel B. Finan and I am confused why they set it up like this:

The problem reads: A loan is being repaid with 16 quarterly payments, where the first 8 payments are each $200 and the last 8 payments are each $400. If the nominal rate of interest convertible quarterly is 10%, use both the prospective method and the retrospective method to find the outstanding loan balance immediately after the first six payments are made.

Using the prospective method, it was set up like this:
B(p,6) = 200(v + v^2) + 400(v + v^2 + ....+ v^8)

If the question asks for the loan balance after 6th payment shouldn't it be:
200 * (annuity-immediate of n = 10) and not include the 400.

If someone can clarify this, that would be helpful.
Reply With Quote
  #2  
Old 03-17-2018, 07:50 PM
xplicitator xplicitator is offline
Member
SOA
 
Join Date: Sep 2014
College: SFU
Posts: 38
Default

Since on the time diagram, we are at time 6. If you wrote 200 * (annuity immediate with n=10), then you are saying that starting at time 8, only payments of 200 are made. But in reality, at time 6-8, it's still 200, but starting with time 9, payments are 400 each rather than just 200. So 200(v + v^2) accounts for time 6 to 8 and then 400(v + v^2 + ....+ v^8) starting at time 9. Hope that helps!
__________________
P, FM, MFE

VEE: Statistics, Economics, Corporate Finance
Reply With Quote
  #3  
Old 03-17-2018, 08:11 PM
Academic Actuary Academic Actuary is offline
Member
 
Join Date: Sep 2009
Posts: 7,668
Default

Quote:
Originally Posted by xplicitator View Post
Since on the time diagram, we are at time 6. If you wrote 200 * (annuity immediate with n=10), then you are saying that starting at time 8, only payments of 200 are made. But in reality, at time 6-8, it's still 200, but starting with time 9, payments are 400 each rather than just 200. So 200(v + v^2) accounts for time 6 to 8 and then 400(v + v^2 + ....+ v^8) starting at time 9. Hope that helps!
You need a v^2 multiplying the second series.
Reply With Quote
  #4  
Old 03-17-2018, 09:05 PM
xplicitator xplicitator is offline
Member
SOA
 
Join Date: Sep 2014
College: SFU
Posts: 38
Default


Yes that I forgot! That v^2 in front of the 400 series is to discount for the 200 time payments.
__________________
P, FM, MFE

VEE: Statistics, Economics, Corporate Finance
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 06:28 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 0.27289 seconds with 11 queries